Notice (8): Undefined offset: 0 [APP/Controller/Component/CommonComponent.php, line 4308]
Code Context
                                    'name_check LIKE'=>strtolower($get_between[1])
                                )));
                                $array_get_word = $get_word['Listnumber'][0]['words'];
$clone = array(
	'id' => '9017',
	'chart' => '',
	'question_id' => '38354',
	'clone_type' => '1',
	'phpfile' => null,
	'clone_symbol' => null,
	'clone_content' => '$(Four) years ago, $(Will)'s age was $(n25)% of $(Ray)'s age. $(Eight) years from their current age, $(Will)'s age will be $(n37.5)% of $(Ray)'s age. How many years is $(Ray) older than $(Will)?',
	'clone_solution_step' => '<table style="height: 181px;" width="504">
<tbody>
<tr>
<td>&nbsp;</td>
<td>$(Will)</td>
<td>$(Ray)</td>
<td>Difference</td>
</tr>
<tr>
<td>Before</td>
<td>$(n1)<sub>x$(n5)</sub> =<br />$(an5) u</td>
<td>$(nn4)<sub>x$(n5)</sub> =<br />$(an20) u</td>
<td><strong>$(an3)<sub>x$(n5)</sub> =</strong><br /><strong>$(an15) u</strong></td>
</tr>
<tr>
<td>Change</td>
<td>+ $(n4)<br />+ $(n8)</td>
<td>+ $(n4)<br />+ $(n8)</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>After</td>
<td>$(n3)<sub>x$(an3)</sub> =<br />$(an9) u</td>
<td>&nbsp;$(nn8)<sub>x$(an3)</sub> =<br />$(an24) u</td>
<td><strong>$(n5)<sub>x$(an3)</sub> =</strong><br /><strong>$(an15) u</strong></td>
</tr>
</tbody>
</table>
$(n25)% = <span class="frac"><sup>$(n25)</sup><sub>100</sub></span> = <span class="frac"><sup>$(n1)</sup><sub>$(nn4)</sub></span><br /> $(n37.5)% = <span class="frac"><sup>$(n375)</sup><sub>1000</sub></span> = <span class="frac"><sup>$(n3)</sup><sub>$(nn8)</sub></span><br /><br />The difference in the ages between $(Will) and $(Ray) remains unchanged. Make the difference the same. LCM of $(an3) and $(n5) is $(an15).<br /><br />Increase in $(Will)'s age <br />= $(an9) u - $(an5) u <br />= $(cn4) u<br /> <br /> $(cn4) u = $(n4) + $(n8) <br />$(cn4) u = $(mn12)<br /><br />1 u = $(mn12) &divide; $(cn4) = $(fn3)<br /> <br />Number of years that $(Ray) is older than $(Will)<br />= $(an20) u - $(an5) u<br />= $(an15) u <br />= $(an15) x $(fn3) <br />= $(n45)<br /> <br /> Answer(s): $(n45)',
	'clone_answer' => '$(n45)														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     ',
	'array' => object(stdClass) {
		1527819843413 => object(stdClass) {}
		1527819923888 => object(stdClass) {}
		1527822711300 => object(stdClass) {}
		1527819889160 => object(stdClass) {}
		1527819895766 => object(stdClass) {}
		1527819858347 => object(stdClass) {}
		1671505785403 => object(stdClass) {}
	},
	'clone_image' => null,
	'clone_solution_step_image' => null,
	'clone_answer_image' => null,
	'status' => true,
	'created' => '2018-04-16 19:33:03',
	'modified' => '2022-12-20 11:17:16',
	'original_question' => 'Four years ago, Will's age was 25% of Ray's age. Eight years from their current age, Will's age will be 37.5% of Ray's age. How many years is Ray older than Will?',
	'formula' => array(
		(int) 0 => 'array_get_words(2,number,$(n4))=$(Four) ',
		(int) 1 => '',
		(int) 2 => 'print_fraction($(n25),100)=$(f1) ',
		(int) 3 => 'simplify_fraction($(f1))=$(f2) ',
		(int) 4 => 'get_denominator($(f2))=$(nn4) ',
		(int) 5 => 'get_numerator($(f2))=$(n1) ',
		(int) 6 => '$(n37.5)*10=$(n375)',
		(int) 7 => 'print_fraction($(n375),1000)=$(f3) ',
		(int) 8 => 'simplify_fraction($(f3))=$(f4) ',
		(int) 9 => 'get_denominator($(f4))=$(nn8) ',
		(int) 10 => 'get_numerator($(f4))=$(n3) ',
		(int) 11 => 'if(equal($(n3)=$(n375))) back',
		(int) 12 => '$(nn4)-$(n1)=$(an3)',
		(int) 13 => '$(nn8)-$(n3)=$(n5)',
		(int) 14 => '',
		(int) 15 => '$(an3)*$(n5) = $(an15)',
		(int) 16 => '',
		(int) 17 => '$(nn4)*$(n5) = $(an20)',
		(int) 18 => '$(n1)*$(n5) = $(an5)',
		(int) 19 => '$(nn8)*$(an3) = $(an24)',
		(int) 20 => '$(n3)*$(an3) = $(an9)',
		(int) 21 => '$(an9) - $(an5)= $(cn4)',
		(int) 22 => 'if(more_than($(cn4)>1)) continue',
		(int) 23 => '',
		(int) 24 => '$(cn4)* $(fn3)=$(mn12)',
		(int) 25 => '$(mn12) -$(n4) = $(n8)',
		(int) 26 => 'if(less_than($(n8)<20)) continue',
		(int) 27 => '$(an15) *$(fn3)  = $(n45)',
		(int) 28 => 'array_get_words(2,number,$(n8))=$(Eight) ',
		(int) 29 => '$(an24)*$(fn3) = $(test)',
		(int) 30 => 'if(more_than($(test)>95)) back',
		(int) 31 => 'if(equal($(n4)=$(n8))) back'
	),
	'time_value' => array(
		(int) 0 => '1527819951583',
		(int) 1 => '1527822361315',
		(int) 2 => '1527821974913',
		(int) 3 => '1527819954449',
		(int) 4 => '1527819954202',
		(int) 5 => '1527819954065',
		(int) 6 => '1527819953829',
		(int) 7 => '1527819953696',
		(int) 8 => '1527819953445',
		(int) 9 => '1527819953326',
		(int) 10 => '1527820287672',
		(int) 11 => '1527820287419',
		(int) 12 => '1527820683516',
		(int) 13 => '1527820683239',
		(int) 14 => '1527820865254',
		(int) 15 => '1527820865001',
		(int) 16 => '1527822303285',
		(int) 17 => '1527820864882',
		(int) 18 => '1527820683157',
		(int) 19 => '1527820287311',
		(int) 20 => '1527821018867',
		(int) 21 => '1527821018591',
		(int) 22 => '1527821018487',
		(int) 23 => '1527821018231',
		(int) 24 => '1527821018127',
		(int) 25 => '1527821454205',
		(int) 26 => '1527822593773',
		(int) 27 => '1527821454020',
		(int) 28 => '1527822119557',
		(int) 29 => '1671504239699',
		(int) 30 => '1671504283610',
		(int) 31 => '1671505342739'
	),
	'criterion' => array(
		(int) 0 => '',
		(int) 1 => '',
		(int) 2 => '',
		(int) 3 => '',
		(int) 4 => '',
		(int) 5 => '',
		(int) 6 => '',
		(int) 7 => '',
		(int) 8 => '',
		(int) 9 => '',
		(int) 10 => '',
		(int) 11 => '',
		(int) 12 => '',
		(int) 13 => '',
		(int) 14 => '',
		(int) 15 => '',
		(int) 16 => '',
		(int) 17 => '',
		(int) 18 => '',
		(int) 19 => '',
		(int) 20 => '',
		(int) 21 => '',
		(int) 22 => '',
		(int) 23 => '',
		(int) 24 => '',
		(int) 25 => '',
		(int) 26 => '',
		(int) 27 => '',
		(int) 28 => '',
		(int) 29 => '',
		(int) 30 => '',
		(int) 31 => ''
	),
	'type_criterion' => array(
		(int) 0 => '',
		(int) 1 => '',
		(int) 2 => '',
		(int) 3 => '',
		(int) 4 => '',
		(int) 5 => '',
		(int) 6 => '',
		(int) 7 => '',
		(int) 8 => '',
		(int) 9 => '',
		(int) 10 => '',
		(int) 11 => '',
		(int) 12 => '',
		(int) 13 => '',
		(int) 14 => '',
		(int) 15 => '',
		(int) 16 => '',
		(int) 17 => '',
		(int) 18 => '',
		(int) 19 => '',
		(int) 20 => '',
		(int) 21 => '',
		(int) 22 => '',
		(int) 23 => '',
		(int) 24 => '',
		(int) 25 => '',
		(int) 26 => '',
		(int) 27 => '',
		(int) 28 => '',
		(int) 29 => '',
		(int) 30 => '',
		(int) 31 => ''
	),
	'image_gridline' => '',
	'code_gridline' => '',
	'level' => '',
	'topic_id' => '',
	'source' => '',
	'question_code' => 'P5.PC.JC.17083300-A1',
	'tag' => '',
	'mark' => '',
	'text_working' => '["","","","","","","","","","","","","","","if(less_than($(n3)<40)) continue","","if(less_than($(an15)<20)) continue","","","","","","","$(mn12) \u00f7 $(cn4) = $(fn3)","","if(whole_number($(fn3))) continue","","","if(less_than($(n45)<60)) continue","","",""]',
	'original_solution' => '25% = <span class="frac"><sup>25</sup><sub>100</sub></span> = <span class="frac"><sup>1</sup><sub>4</sub></span><br /> 37.5% = <span class="frac"><sup>375</sup><sub>100</sub></span> = <span class="frac"><sup>3</sup><sub>8</sub></span><br /> <br /> The difference in the ages between Will and Ray remains unchanged. Make the difference the same.<br /> Will : Ray : Difference<br /> 1 : 4 : 3 (x5)<br /> 5 : 20 : 15<br /> <br /> Will : Ray : Difference<br /> 3 : 8 : 5 (x3)<br /> 9 : 24 : 15<br /> <br /> Change in Will's age = 9 u - 5 u = 4 u<br /> <br /> 4 u = 8 + 4 = 12<br /> 1 u = 12 &divide; 4 = 3<br /> <br /> Difference between Ray and Will's age = 15 u = 15 x 3 = 45<br /> <br /> Answer(s): 45',
	'delete_by' => null,
	'delete_date' => null
)
$Array1 = object(Array1) {
	table => 'array1s'
	validate => array()
	useDbConfig => 'default'
	useTable => 'array1s'
	id => '61'
	data => array()
	schemaName => 'ischoolb_orgi'
	primaryKey => 'id'
	validationErrors => array()
	validationDomain => null
	tablePrefix => ''
	plugin => null
	name => 'Array1'
	alias => 'Array1'
	tableToModel => array(
		'array1s' => 'Array1'
	)
	cacheQueries => false
	belongsTo => array()
	hasOne => array()
	hasMany => array()
	hasAndBelongsToMany => array()
	actsAs => null
	Behaviors => object(BehaviorCollection) {}
	whitelist => array()
	cacheSources => true
	findQueryType => null
	recursive => (int) 1
	order => null
	virtualFields => array()
	__backAssociation => array()
	__backInnerAssociation => array()
	__backOriginalAssociation => array()
	__backContainableAssociation => array()
	__safeUpdateMode => false
	useConsistentAfterFind => true
	findMethods => array(
		'all' => true,
		'first' => true,
		'count' => true,
		'neighbors' => true,
		'list' => true,
		'threaded' => true
	)
	[protected] _schema => array(
		'id' => array(
			[maximum depth reached]
		),
		'name' => array(
			[maximum depth reached]
		),
		'content' => array(
			[maximum depth reached]
		),
		'note' => array(
			[maximum depth reached]
		),
		'created' => array(
			[maximum depth reached]
		),
		'modified' => array(
			[maximum depth reached]
		)
	)
	[protected] _associationKeys => array(
		'belongsTo' => array(
			[maximum depth reached]
		),
		'hasOne' => array(
			[maximum depth reached]
		),
		'hasMany' => array(
			[maximum depth reached]
		),
		'hasAndBelongsToMany' => array(
			[maximum depth reached]
		)
	)
	[protected] _associations => array(
		(int) 0 => 'belongsTo',
		(int) 1 => 'hasOne',
		(int) 2 => 'hasMany',
		(int) 3 => 'hasAndBelongsToMany'
	)
	[protected] _insertID => null
	[protected] _sourceConfigured => true
	[protected] _eventManager => object(CakeEventManager) {}
	[protected] _validator => null
}
$Prime = object(AppModel) {
	useDbConfig => 'default'
	useTable => 'primes'
	id => false
	data => array()
	schemaName => null
	table => 'primes'
	primaryKey => 'id'
	validate => array()
	validationErrors => array()
	validationDomain => null
	plugin => null
	name => 'Prime'
	alias => 'Prime'
	tableToModel => array(
		'primes' => 'Prime'
	)
	cacheQueries => false
	belongsTo => array()
	hasOne => array()
	hasMany => array()
	hasAndBelongsToMany => array()
	actsAs => null
	Behaviors => object(BehaviorCollection) {}
	whitelist => array()
	cacheSources => true
	findQueryType => null
	recursive => (int) 1
	order => null
	virtualFields => array()
	__backAssociation => array()
	__backInnerAssociation => array()
	__backOriginalAssociation => array()
	__backContainableAssociation => array()
	__safeUpdateMode => false
	useConsistentAfterFind => true
	findMethods => array(
		'all' => true,
		'first' => true,
		'count' => true,
		'neighbors' => true,
		'list' => true,
		'threaded' => true
	)
	[protected] _schema => null
	[protected] _associationKeys => array(
		'belongsTo' => array(
			[maximum depth reached]
		),
		'hasOne' => array(
			[maximum depth reached]
		),
		'hasMany' => array(
			[maximum depth reached]
		),
		'hasAndBelongsToMany' => array(
			[maximum depth reached]
		)
	)
	[protected] _associations => array(
		(int) 0 => 'belongsTo',
		(int) 1 => 'hasOne',
		(int) 2 => 'hasMany',
		(int) 3 => 'hasAndBelongsToMany'
	)
	[protected] _insertID => null
	[protected] _sourceConfigured => false
	[protected] _eventManager => null
	[protected] _validator => null
}
$answer_fix = '$(n45)														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     '
$count_crition = (int) 8
$count_array_break = (int) 0
$count_variable_nnt = (int) 0
$message_nnt = ''
$field = 'time_value'
$array_get = array(
	(int) 6 => 'n37.5',
	(int) 2 => 'n25',
	(int) 0 => 'n4',
	(int) 25 => 'n4',
	(int) 31 => 'n4',
	(int) 24 => 'fn3',
	(int) 27 => 'fn3',
	(int) 29 => 'fn3',
	(int) 3 => '(f1)',
	(int) 4 => '(f2)',
	(int) 5 => '(f2)',
	(int) 12 => '(nn4)',
	(int) 17 => '(nn4)',
	(int) 18 => '(n1)',
	(int) 7 => '(n375)',
	(int) 11 => '(n375)',
	(int) 8 => '(f3)',
	(int) 9 => '(f4)',
	(int) 10 => '(f4)',
	(int) 13 => '(nn8)',
	(int) 19 => '(nn8)',
	(int) 20 => '(n3)',
	(int) 15 => '(an3)',
	(int) 21 => '(an5)',
	(int) 22 => '(cn4)',
	(int) 26 => '(n8)',
	(int) 28 => '(n8)'
)
$tempt = array(
	(int) 0 => '10',
	(int) 1 => '25',
	(int) 2 => '20'
)
$list_name_array = array(
	(int) 0 => 'David',
	(int) 1 => 'Bryan'
)
$list_array_item = array(
	'Will' => array(
		'listArray' => array(
			(int) 0 => 'Caden',
			(int) 1 => 'Luis',
			(int) 2 => 'Vaidev',
			(int) 3 => 'Archie',
			(int) 4 => 'Cole',
			(int) 5 => 'Julian',
			(int) 6 => 'Jeremy',
			(int) 7 => 'Seth',
			(int) 8 => 'Pierre',
			(int) 9 => 'Japheth',
			(int) 10 => 'Neave',
			(int) 11 => 'Jenson',
			(int) 12 => 'Brandon',
			(int) 13 => 'Tom',
			(int) 14 => 'Ahmad',
			(int) 15 => 'Bryan',
			(int) 16 => 'Ryan',
			(int) 17 => 'Asher',
			(int) 18 => 'Ben',
			(int) 19 => 'Carl',
			(int) 20 => 'David',
			(int) 21 => 'Ethan',
			(int) 22 => 'Fred',
			(int) 23 => 'George',
			(int) 24 => 'Henry',
			(int) 25 => 'Ian',
			(int) 26 => 'Jack',
			(int) 27 => 'Ken',
			(int) 28 => 'Liam',
			(int) 29 => 'Mark',
			(int) 30 => 'Nick',
			(int) 31 => 'Oscar',
			(int) 32 => 'Peter',
			(int) 33 => 'Rael',
			(int) 34 => 'Sean',
			(int) 35 => 'Tim',
			(int) 36 => 'Vincent',
			(int) 37 => 'Will',
			(int) 38 => 'Xavier',
			(int) 39 => 'Zane',
			(int) 40 => 'Albert',
			(int) 41 => 'Andy',
			(int) 42 => 'Bobby',
			(int) 43 => 'Billy',
			(int) 44 => 'Charlie',
			(int) 45 => 'Cody',
			(int) 46 => 'Daniel',
			(int) 47 => 'Dylan',
			(int) 48 => 'Eric',
			(int) 49 => 'Elijah',
			(int) 50 => 'Fabian',
			(int) 51 => 'Flynn',
			(int) 52 => 'Gabriel',
			(int) 53 => 'Glen',
			(int) 54 => 'Harry',
			(int) 55 => 'Howard',
			(int) 56 => 'Ivan',
			(int) 57 => 'John',
			(int) 58 => 'Justin',
			(int) 59 => 'Luke',
			(int) 60 => 'Lee',
			(int) 61 => 'Michael',
			(int) 62 => 'Owen',
			(int) 63 => 'Oliver',
			(int) 64 => 'Paul',
			(int) 65 => 'Perry',
			(int) 66 => 'Riordan',
			(int) 67 => 'Reggie',
			(int) 68 => 'Sam',
			(int) 69 => 'Simon',
			(int) 70 => 'Tommy',
			(int) 71 => 'Valen',
			(int) 72 => 'Wesley',
			(int) 73 => 'Warren',
			(int) 74 => 'Zeph'
		),
		'keyArray' => (int) 20,
		'manyArray' => '1',
		'capitalize' => '0'
	),
	'Ray' => array(
		'listArray' => array(
			(int) 0 => 'Caden',
			(int) 1 => 'Luis',
			(int) 2 => 'Vaidev',
			(int) 3 => 'Archie',
			(int) 4 => 'Cole',
			(int) 5 => 'Julian',
			(int) 6 => 'Jeremy',
			(int) 7 => 'Seth',
			(int) 8 => 'Pierre',
			(int) 9 => 'Japheth',
			(int) 10 => 'Neave',
			(int) 11 => 'Jenson',
			(int) 12 => 'Brandon',
			(int) 13 => 'Tom',
			(int) 14 => 'Ahmad',
			(int) 15 => 'Bryan',
			(int) 16 => 'Ryan',
			(int) 17 => 'Asher',
			(int) 18 => 'Ben',
			(int) 19 => 'Carl',
			(int) 20 => 'David',
			(int) 21 => 'Ethan',
			(int) 22 => 'Fred',
			(int) 23 => 'George',
			(int) 24 => 'Henry',
			(int) 25 => 'Ian',
			(int) 26 => 'Jack',
			(int) 27 => 'Ken',
			(int) 28 => 'Liam',
			(int) 29 => 'Mark',
			(int) 30 => 'Nick',
			(int) 31 => 'Oscar',
			(int) 32 => 'Peter',
			(int) 33 => 'Rael',
			(int) 34 => 'Sean',
			(int) 35 => 'Tim',
			(int) 36 => 'Vincent',
			(int) 37 => 'Will',
			(int) 38 => 'Xavier',
			(int) 39 => 'Zane',
			(int) 40 => 'Albert',
			(int) 41 => 'Andy',
			(int) 42 => 'Bobby',
			(int) 43 => 'Billy',
			(int) 44 => 'Charlie',
			(int) 45 => 'Cody',
			(int) 46 => 'Daniel',
			(int) 47 => 'Dylan',
			(int) 48 => 'Eric',
			(int) 49 => 'Elijah',
			(int) 50 => 'Fabian',
			(int) 51 => 'Flynn',
			(int) 52 => 'Gabriel',
			(int) 53 => 'Glen',
			(int) 54 => 'Harry',
			(int) 55 => 'Howard',
			(int) 56 => 'Ivan',
			(int) 57 => 'John',
			(int) 58 => 'Justin',
			(int) 59 => 'Luke',
			(int) 60 => 'Lee',
			(int) 61 => 'Michael',
			(int) 62 => 'Owen',
			(int) 63 => 'Oliver',
			(int) 64 => 'Paul',
			(int) 65 => 'Perry',
			(int) 66 => 'Riordan',
			(int) 67 => 'Reggie',
			(int) 68 => 'Sam',
			(int) 69 => 'Simon',
			(int) 70 => 'Tommy',
			(int) 71 => 'Valen',
			(int) 72 => 'Wesley',
			(int) 73 => 'Warren',
			(int) 74 => 'Zeph'
		),
		'keyArray' => (int) 15,
		'manyArray' => '1',
		'capitalize' => '0'
	)
)
$list_italic = array()
$array_variable = object(stdClass) {
	1527819843413 => object(stdClass) {}
	1527819923888 => object(stdClass) {}
	1527822711300 => object(stdClass) {}
	1527819889160 => object(stdClass) {}
	1527819895766 => object(stdClass) {}
	1527819858347 => object(stdClass) {}
	1671505785403 => object(stdClass) {}
}
$question_content = '$(Four) years ago, $(Will)'s age was $(n25)% of $(Ray)'s age. $(Eight) years from their current age, $(Will)'s age will be $(n37.5)% of $(Ray)'s age. How many years is $(Ray) older than $(Will)?'
$solution_step = '<table style="height: 181px;" width="504">
<tbody>
<tr>
<td>&nbsp;</td>
<td>$(Will)</td>
<td>$(Ray)</td>
<td>Difference</td>
</tr>
<tr>
<td>Before</td>
<td>$(n1)<sub>x$(n5)</sub> =<br />$(an5) u</td>
<td>$(nn4)<sub>x$(n5)</sub> =<br />$(an20) u</td>
<td><strong>$(an3)<sub>x$(n5)</sub> =</strong><br /><strong>$(an15) u</strong></td>
</tr>
<tr>
<td>Change</td>
<td>+ $(n4)<br />+ $(n8)</td>
<td>+ $(n4)<br />+ $(n8)</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>After</td>
<td>$(n3)<sub>x$(an3)</sub> =<br />$(an9) u</td>
<td>&nbsp;$(nn8)<sub>x$(an3)</sub> =<br />$(an24) u</td>
<td><strong>$(n5)<sub>x$(an3)</sub> =</strong><br /><strong>$(an15) u</strong></td>
</tr>
</tbody>
</table>
$(n25)% = <span class="frac"><sup>$(n25)</sup><sub>100</sub></span> = <span class="frac"><sup>$(n1)</sup><sub>$(nn4)</sub></span><br /> $(n37.5)% = <span class="frac"><sup>$(n375)</sup><sub>1000</sub></span> = <span class="frac"><sup>$(n3)</sup><sub>$(nn8)</sub></span><br /><br />The difference in the ages between $(Will) and $(Ray) remains unchanged. Make the difference the same. LCM of $(an3) and $(n5) is $(an15).<br /><br />Increase in $(Will)'s age <br />= $(an9) u - $(an5) u <br />= $(cn4) u<br /> <br /> $(cn4) u = $(n4) + $(n8) <br />$(cn4) u = $(mn12)<br /><br />1 u = $(mn12) &divide; $(cn4) = $(fn3)<br /> <br />Number of years that $(Ray) is older than $(Will)<br />= $(an20) u - $(an5) u<br />= $(an15) u <br />= $(an15) x $(fn3) <br />= $(n45)<br /> <br /> Answer(s): $(n45)'
$clone_answer = '$(n45)														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     														     '
$formula = array(
	(int) 0 => 'array_get_words(2,number,5)=Five',
	(int) 1 => '',
	(int) 2 => 'print_fraction(25,100)=25/100',
	(int) 3 => 'simplify_fraction(25/100)=1/4',
	(int) 4 => 'get_denominator(1/4)=4',
	(int) 5 => 'get_numerator(1/4)=1',
	(int) 6 => '37.5*10=375',
	(int) 7 => 'print_fraction(375,1000)=375/1000',
	(int) 8 => 'simplify_fraction(375/1000)=3/8',
	(int) 9 => 'get_denominator(3/8)=8',
	(int) 10 => 'get_numerator(3/8)=3',
	(int) 11 => 'if(equal(3=375))back',
	(int) 12 => '4-1=3',
	(int) 13 => '8-3=5',
	(int) 14 => '',
	(int) 15 => '3*5=15',
	(int) 16 => '',
	(int) 17 => '4*5=20',
	(int) 18 => '1*5=5',
	(int) 19 => '8*3=24',
	(int) 20 => '3*3=9',
	(int) 21 => '9-5=4',
	(int) 22 => 'if(more_than(4>1))continue',
	(int) 23 => '',
	(int) 24 => '4*1=4',
	(int) 25 => '4-5=-1',
	(int) 26 => 'if(less_than(-1<20))continue',
	(int) 27 => '15*1=15',
	(int) 28 => 'array_get_words(2,number,-1)=$(Eight)',
	(int) 29 => '24*1=$(test)',
	(int) 30 => 'if(more_than($(test)>95))back',
	(int) 31 => 'if(equal(5=-1))back'
)
$formula_1 = array(
	(int) 0 => 'array_get_words(2,number,$(n4))=$(Four) ',
	(int) 1 => '',
	(int) 2 => 'print_fraction($(n25),100)=$(f1) ',
	(int) 3 => 'simplify_fraction($(f1))=$(f2) ',
	(int) 4 => 'get_denominator($(f2))=$(nn4) ',
	(int) 5 => 'get_numerator($(f2))=$(n1) ',
	(int) 6 => '$(n37.5)*10=$(n375)',
	(int) 7 => 'print_fraction($(n375),1000)=$(f3) ',
	(int) 8 => 'simplify_fraction($(f3))=$(f4) ',
	(int) 9 => 'get_denominator($(f4))=$(nn8) ',
	(int) 10 => 'get_numerator($(f4))=$(n3) ',
	(int) 11 => 'if(equal($(n3)=$(n375))) back',
	(int) 12 => '$(nn4)-$(n1)=$(an3)',
	(int) 13 => '$(nn8)-$(n3)=$(n5)',
	(int) 14 => '',
	(int) 15 => '$(an3)*$(n5) = $(an15)',
	(int) 16 => '',
	(int) 17 => '$(nn4)*$(n5) = $(an20)',
	(int) 18 => '$(n1)*$(n5) = $(an5)',
	(int) 19 => '$(nn8)*$(an3) = $(an24)',
	(int) 20 => '$(n3)*$(an3) = $(an9)',
	(int) 21 => '$(an9) - $(an5)= $(cn4)',
	(int) 22 => 'if(more_than($(cn4)>1)) continue',
	(int) 23 => '',
	(int) 24 => '$(cn4)* $(fn3)=$(mn12)',
	(int) 25 => '$(mn12) -$(n4) = $(n8)',
	(int) 26 => 'if(less_than($(n8)<20)) continue',
	(int) 27 => '$(an15) *$(fn3)  = $(n45)',
	(int) 28 => 'array_get_words(2,number,$(n8))=$(Eight) ',
	(int) 29 => '$(an24)*$(fn3) = $(test)',
	(int) 30 => 'if(more_than($(test)>95)) back',
	(int) 31 => 'if(equal($(n4)=$(n8))) back'
)
$criterion = array(
	(int) 0 => '',
	(int) 1 => '',
	(int) 2 => '',
	(int) 3 => '',
	(int) 4 => '',
	(int) 5 => '',
	(int) 6 => '',
	(int) 7 => '',
	(int) 8 => '',
	(int) 9 => '',
	(int) 10 => '',
	(int) 11 => '',
	(int) 12 => '',
	(int) 13 => '',
	(int) 14 => '',
	(int) 15 => '',
	(int) 16 => '',
	(int) 17 => '',
	(int) 18 => '',
	(int) 19 => '',
	(int) 20 => '',
	(int) 21 => '',
	(int) 22 => '',
	(int) 23 => '',
	(int) 24 => '',
	(int) 25 => '',
	(int) 26 => '',
	(int) 27 => '',
	(int) 28 => '',
	(int) 29 => '',
	(int) 30 => '',
	(int) 31 => ''
)
$type_criterion = array(
	(int) 0 => '',
	(int) 1 => '',
	(int) 2 => '',
	(int) 3 => '',
	(int) 4 => '',
	(int) 5 => '',
	(int) 6 => '',
	(int) 7 => '',
	(int) 8 => '',
	(int) 9 => '',
	(int) 10 => '',
	(int) 11 => '',
	(int) 12 => '',
	(int) 13 => '',
	(int) 14 => '',
	(int) 15 => '',
	(int) 16 => '',
	(int) 17 => '',
	(int) 18 => '',
	(int) 19 => '',
	(int) 20 => '',
	(int) 21 => '',
	(int) 22 => '',
	(int) 23 => '',
	(int) 24 => '',
	(int) 25 => '',
	(int) 26 => '',
	(int) 27 => '',
	(int) 28 => '',
	(int) 29 => '',
	(int) 30 => '',
	(int) 31 => ''
)
$time_value = array(
	(int) 0 => '1527819951583',
	(int) 1 => '1527822361315',
	(int) 2 => '1527821974913',
	(int) 3 => '1527819954449',
	(int) 4 => '1527819954202',
	(int) 5 => '1527819954065',
	(int) 6 => '1527819953829',
	(int) 7 => '1527819953696',
	(int) 8 => '1527819953445',
	(int) 9 => '1527819953326',
	(int) 10 => '1527820287672',
	(int) 11 => '1527820287419',
	(int) 12 => '1527820683516',
	(int) 13 => '1527820683239',
	(int) 14 => '1527820865254',
	(int) 15 => '1527820865001',
	(int) 16 => '1527822303285',
	(int) 17 => '1527820864882',
	(int) 18 => '1527820683157',
	(int) 19 => '1527820287311',
	(int) 20 => '1527821018867',
	(int) 21 => '1527821018591',
	(int) 22 => '1527821018487',
	(int) 23 => '1527821018231',
	(int) 24 => '1527821018127',
	(int) 25 => '1527821454205',
	(int) 26 => '1527822593773',
	(int) 27 => '1527821454020',
	(int) 28 => '1527822119557',
	(int) 29 => '1671504239699',
	(int) 30 => '1671504283610',
	(int) 31 => '1671505342739'
)
$k = '1671505785403'
$v = object(stdClass) {
	cate => 'whole_number'
	name => 'fn3'
	range => object(stdClass) {}
	attr => object(stdClass) {}
}
$array_system = array(
	(int) 0 => 'Caden',
	(int) 1 => 'Luis',
	(int) 2 => 'Vaidev',
	(int) 3 => 'Archie',
	(int) 4 => 'Cole',
	(int) 5 => 'Julian',
	(int) 6 => 'Jeremy',
	(int) 7 => 'Seth',
	(int) 8 => 'Pierre',
	(int) 9 => 'Japheth',
	(int) 10 => 'Neave',
	(int) 11 => 'Jenson',
	(int) 12 => 'Brandon',
	(int) 13 => 'Tom',
	(int) 14 => 'Ahmad',
	(int) 15 => 'Bryan',
	(int) 16 => 'Ryan',
	(int) 17 => 'Asher',
	(int) 18 => 'Ben',
	(int) 19 => 'Carl',
	(int) 20 => 'David',
	(int) 21 => 'Ethan',
	(int) 22 => 'Fred',
	(int) 23 => 'George',
	(int) 24 => 'Henry',
	(int) 25 => 'Ian',
	(int) 26 => 'Jack',
	(int) 27 => 'Ken',
	(int) 28 => 'Liam',
	(int) 29 => 'Mark',
	(int) 30 => 'Nick',
	(int) 31 => 'Oscar',
	(int) 32 => 'Peter',
	(int) 33 => 'Rael',
	(int) 34 => 'Sean',
	(int) 35 => 'Tim',
	(int) 36 => 'Vincent',
	(int) 37 => 'Will',
	(int) 38 => 'Xavier',
	(int) 39 => 'Zane',
	(int) 40 => 'Albert',
	(int) 41 => 'Andy',
	(int) 42 => 'Bobby',
	(int) 43 => 'Billy',
	(int) 44 => 'Charlie',
	(int) 45 => 'Cody',
	(int) 46 => 'Daniel',
	(int) 47 => 'Dylan',
	(int) 48 => 'Eric',
	(int) 49 => 'Elijah',
	(int) 50 => 'Fabian',
	(int) 51 => 'Flynn',
	(int) 52 => 'Gabriel',
	(int) 53 => 'Glen',
	(int) 54 => 'Harry',
	(int) 55 => 'Howard',
	(int) 56 => 'Ivan',
	(int) 57 => 'John',
	(int) 58 => 'Justin',
	(int) 59 => 'Luke',
	(int) 60 => 'Lee',
	(int) 61 => 'Michael',
	(int) 62 => 'Owen',
	(int) 63 => 'Oliver',
	(int) 64 => 'Paul',
	(int) 65 => 'Perry',
	(int) 66 => 'Riordan',
	(int) 67 => 'Reggie',
	(int) 68 => 'Sam',
	(int) 69 => 'Simon',
	(int) 70 => 'Tommy',
	(int) 71 => 'Valen',
	(int) 72 => 'Wesley',
	(int) 73 => 'Warren',
	(int) 74 => 'Zeph'
)
$dem_array_trung = (int) 1
$value_rand_check = (int) 15
$value_check = 'Bryan'
$tempt_array = array(
	(int) 0 => '10',
	(int) 1 => '25',
	(int) 2 => '20'
)
$tempt_k = (int) 2
$tempt_v = '20'
$check_who_nnt = (int) 0
$from = '1'
$to = '10'
$teapt_variable = array(
	(int) 0 => '37.5'
)
$place = '1'
$dem_while = (int) 1
$key_rand = (float) 0
$count_dp = (int) 1
$arr_variable = array(
	'Will' => 'David',
	'n37.5' => (float) 37.5,
	'n25' => '25',
	'n4' => (int) 5,
	'k' => (int) 9,
	'Ray' => 'Bryan',
	'fn3' => (int) 1,
	'(Four)' => 'Five',
	'(f1)' => '25/100',
	'(f2)' => '1/4',
	'(nn4)' => (int) 4,
	'(n1)' => (int) 1,
	'(n375)' => (float) 375,
	'(f3)' => '375/1000',
	'(f4)' => '3/8',
	'(nn8)' => (int) 8,
	'(n3)' => (int) 3,
	'(an3)' => (int) 3,
	'(n5)' => (int) 5,
	'(an15)' => (int) 15,
	'(an20)' => (int) 20,
	'(an5)' => (int) 5,
	'(an24)' => (int) 24,
	'(an9)' => (int) 9,
	'(cn4)' => (int) 4,
	'(mn12)' => (int) 4,
	'(n8)' => (int) -1,
	'(n45)' => (int) 15
)
$variable_k = '(n45)'
$variable_v = '15'
$formula_k = (int) 28
$formula_v = 'array_get_words(2,number,$(n8))=$(Eight)'
$criterion_k = (int) 31
$criterion_v = ''
$type_criterion_k = (int) 31
$type_criterion_v = ''
$variable_show = array(
	'Will' => 'David',
	'n37.5' => (float) 37.5,
	'n25' => '25',
	'n4' => (int) 5,
	'k' => (int) 9,
	'Ray' => 'Bryan',
	'fn3' => (int) 1
)
$start = 'array_get_words('
$end = ')'
$array_mixed_nnt = array()
$check_changes = 'if(equal(5=-1))back'
$criterion_continue = '$(Eight)'
$criterion_back = 'ght)'
$type_criterion_action = (int) 1
$get_between = array(
	(int) 0 => '2',
	(int) 1 => 'number',
	(int) 2 => '-1'
)
$type_cri = 'less_than'
$get_between_value = '-1<20'
$bieuthuc = array(
	(int) 0 => 'array_get_words(2,number,-1)',
	(int) 1 => '(Eight)'
)
$substr_pos = 'change_decimal_to_fraction'
$get_numerator = false
$get_whole_number_nnt = false
$pos = false
$giatri = (int) 15
$substr_simplify_frac = 'simplify_fraction'
$simplify_frac = false
$substr_simplify_ratio = 'simplify_ratio'
$simplify_ratio = false
$substr_get_element_of_ratio = 'get_element'
$get_element_of_ratio = false
$substr_numberto2decimal = 'change_number_to_2dp'
$change_to_2dp = false
$substr_digit_5_0 = 'change_to_2dp_with_5_or_0'
$change_to_2dp_5_or_0 = false
$substr_mixed_num = 'change_improper_to_mixed_number'
$mixed_num = false
$substr_mixed_to_improper = 'change_mixed_number_to_improper'
$mixed_to_improper = false
$substr_invert_fraction = 'invert_fraction'
$invert_fraction = false
$substr_get_same_numerator = 'share_same_numerator'
$get_same_numerator = false
$substr_get_same_denominator = 'share_same_denominator'
$get_same_denominator = false
$substr_reduce_into_ratio = 'simplify_any_into_ratio'
$reduce_into_ratio = false
$substr_multiply_subscript = 'multiply_ratio_subscript'
$multiply_subscript = false
$substr_assign = 'assign'
$assign = false
$substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm'
$is_12_hour_time_am_pm = false
$substr_is_2400_hour_time = 'get_2400_hour_time'
$is_2400_hour_time = false
$substr_add_or_minus_time = 'add_or_minus_min_or_s'
$add_or_minus_time = false
$substr_change_percentage_to_frac = 'change_percentage_to_frac'
$change_percentage_to_frac = false
$substr_round_2_decimal = 'round_2_decimal_place'
$round_2_decimal_place = false
$substr_round_1_decimal = 'round_1_decimal_place'
$round_1_decimal_place = false
$substr_get_quotient = 'get_quotient'
$get_quotient = false
$substr_get_remainder = 'get_remainder'
$get_remainder = false
$substr_change_min_to_hour_min = 'change_min_to_h_min'
$change_min_to_hour_min = false
$substr_change_h_min_to_min = 'change_h_min_to_min'
$change_h_min_to_min = false
$substr_carry_1 = 'carry_1_from_mixed_number'
$get_carry_1 = false
$change_d_or_p_to_fraction = 'change_to_unsimplied_fraction'
$get_change_d_or_p_to_fraction = false
$round_off_to_nearest_ten = 'round_off_to_nearest_ten'
$get_round_off_to_nearest_ten = false
$round_off_to_nearest_hundred = 'round_off_to_nearest_hundred'
$get_round_off_to_nearest_hundred = false
$round_off_to_nearest_thousand = 'round_off_to_nearest_thousand'
$get_round_off_to_nearest_thousand = false
$change_12_to_24 = 'change_12h_to_24h'
$get_12_to_24 = false
$change_24_to_12 = 'change_24h_to_12h'
$get_24_to_12 = false
$get_factors = 'get_factors'
$get_factors_nnt = false
$get_common_factors = 'get_common_factors'
$get_common_factors_nnt = false
$get_multiples = 'get_multiples'
$get_multiples_23916 = false
$get_add_or_minus_multiples = 'add_or_minus_multiples'
$add_or_minus_multiples_23916 = false
$get_common_numbers = 'get_common_numbers'
$get_common_numbers_240916 = false
$substr_array_singular = 'array_singular'
$array_singular_101016 = false
$substr_array_plural = 'array_plural'
$array_plural_101016 = false
$substr_print_fraction = 'print_fraction'
$print_fraction_101016 = false
$substr_array_capitalize = 'array_capitalize'
$array_capitalize_101016 = false
$substr_array_get_words = 'array_get_words'
$array_get_words_31316 = (int) 0
$substr_array_get_1st_letter = 'array_get_1st_letter'
$array_array_get_1st_letter = false
$substr_array_get_next_loop = 'array_get_next_loop'
$array_get_next_loop = false
$substr_array_get_next_break = 'array_get_next_break'
$array_get_next_break = false
$substr_multiply_fraction = 'do_fraction'
$array_multiply_fraction = false
$substr_change_to_italic = 'change_to_italic'
$array_change_to_italic = false
$match = array(
	(int) 0 => 'print_fraction(375,1000)',
	(int) 1 => '375,1000',
	(int) 2 => ')'
)
$Arraynumber = object(Arraynumber) {
	validate => array()
	hasMany => array(
		'Listnumber' => array(
			[maximum depth reached]
		)
	)
	useDbConfig => 'default'
	useTable => 'arraynumbers'
	id => false
	data => array()
	schemaName => 'ischoolb_orgi'
	table => 'arraynumbers'
	primaryKey => 'id'
	validationErrors => array()
	validationDomain => null
	tablePrefix => ''
	plugin => null
	name => 'Arraynumber'
	alias => 'Arraynumber'
	tableToModel => array(
		'arraynumbers' => 'Arraynumber',
		'listnumbers' => 'Listnumber'
	)
	cacheQueries => false
	belongsTo => array()
	hasOne => array()
	hasAndBelongsToMany => array()
	actsAs => null
	Behaviors => object(BehaviorCollection) {}
	whitelist => array()
	cacheSources => true
	findQueryType => null
	recursive => (int) 1
	order => null
	virtualFields => array()
	__backAssociation => array()
	__backInnerAssociation => array()
	__backOriginalAssociation => array()
	__backContainableAssociation => array()
	__safeUpdateMode => false
	useConsistentAfterFind => true
	findMethods => array(
		'all' => true,
		'first' => true,
		'count' => true,
		'neighbors' => true,
		'list' => true,
		'threaded' => true
	)
	Listnumber => object(Listnumber) {}
	[protected] _schema => array(
		'id' => array(
			[maximum depth reached]
		),
		'name' => array(
			[maximum depth reached]
		),
		'name_check' => array(
			[maximum depth reached]
		),
		'created' => array(
			[maximum depth reached]
		),
		'modified' => array(
			[maximum depth reached]
		)
	)
	[protected] _associationKeys => array(
		'belongsTo' => array(
			[maximum depth reached]
		),
		'hasOne' => array(
			[maximum depth reached]
		),
		'hasMany' => array(
			[maximum depth reached]
		),
		'hasAndBelongsToMany' => array(
			[maximum depth reached]
		)
	)
	[protected] _associations => array(
		(int) 0 => 'belongsTo',
		(int) 1 => 'hasOne',
		(int) 2 => 'hasMany',
		(int) 3 => 'hasAndBelongsToMany'
	)
	[protected] _insertID => null
	[protected] _sourceConfigured => true
	[protected] _eventManager => object(CakeEventManager) {}
	[protected] _validator => null
}
$get_word = array(
	'Arraynumber' => array(
		'id' => '1',
		'name' => 'number',
		'name_check' => 'number',
		'created' => '2017-04-10 09:37:42',
		'modified' => '2017-06-02 10:26:13'
	),
	'Listnumber' => array()
)
$array_get_word = 'five'
$k1 = (int) 31
$v1 = 'if(equal(5=-1))back'
CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4308
ClonesController::index2() - APP/Controller/ClonesController.php, line 2226
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 119

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Question

Percent of a whole, Percent to units, Percent of different bases, More than or less than, Unchanged difference, Units table

P5.PC.JC.17083300-A1

Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

4 m

{"Will":"David","n37.5":37.5,"n25":"25","n4":5,"k":9,"Ray":"Bryan","fn3":1,"(Four)":"Five","(f1)":"<span class='frac'><sup>25<\/sup><sub>100<\/sub><\/span>","(f2)":"<span class='frac'><sup>1<\/sup><sub>4<\/sub><\/span>","(nn4)":4,"(n1)":1,"(n375)":375,"(f3)":"<span class='frac'><sup>375<\/sup><sub>1000<\/sub><\/span>","(f4)":"<span class='frac'><sup>3<\/sup><sub>8<\/sub><\/span>","(nn8)":8,"(n3)":3,"(an3)":3,"(n5)":5,"(an15)":15,"(an20)":20,"(an5)":5,"(an24)":24,"(an9)":9,"(cn4)":4,"(mn12)":4,"(n8)":-1,"(n45)":15,"(Eight)":"","(test)":24}

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Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

	David	Bryan	Difference
Before	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u
Change	+ 5 + -1	+ 5 + -1
After	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u

25% = ²⁵₁₀₀ = ¹₄
37.5% = ³⁷⁵₁₀₀₀ = ³₈

The difference in the ages between David and Bryan remains unchanged. Make the difference the same. LCM of 3 and 5 is 15.

Increase in David's age
= 9 u - 5 u
= 4 u

4 u = 5 + -1
4 u = 4

1 u = 4 ÷ 4 = 1

Number of years that Bryan is older than David
= 20 u - 5 u
= 15 u
= 15 x 1
= 15

Answer(s): 15

4 m

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Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

{"Will":"David","n37.5":37.5,"n25":"25","n4":5,"k":9,"Ray":"Bryan","fn3":1,"(Four)":"Five","(f1)":"<span class='frac'><sup>25<\/sup><sub>100<\/sub><\/span>","(f2)":"<span class='frac'><sup>1<\/sup><sub>4<\/sub><\/span>","(nn4)":4,"(n1)":1,"(n375)":375,"(f3)":"<span class='frac'><sup>375<\/sup><sub>1000<\/sub><\/span>","(f4)":"<span class='frac'><sup>3<\/sup><sub>8<\/sub><\/span>","(nn8)":8,"(n3)":3,"(an3)":3,"(n5)":5,"(an15)":15,"(an20)":20,"(an5)":5,"(an24)":24,"(an9)":9,"(cn4)":4,"(mn12)":4,"(n8)":-1,"(n45)":15,"(Eight)":"","(test)":24}

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Ischool Pte Ltd

Date:01 Jul 2024

Topic: PERCENTAGE

Question Code: P5.PC.JC.17083300

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Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

(4 m)

Answer(s):

Ischool Pte Ltd

Date: 01 Jul 2024

Topic: PERCENTAGE

Question Code: P5.PC.JC.17083300

Student:

Class:

Level:

School:

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Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

(4 m)

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Primary 5 PERCENTAGE P5.PC.JC.17083300

01 Jul 2024, 05:43 PM

Five years ago, David's age was 25% of Bryan's age. years from their current age, David's age will be 37.5% of Bryan's age. How many years is Bryan older than David?

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ISchool Pte Ltd

Date:01 Jul 2024

Topic:PERCENTAGE

Question Number:P5.PC.JC.17083300-A1

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