- How many gaps will there be between the fifteenth bag and the bag?
- What is the distance between the 15th bag and the 21th bag?
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)));
$array_get_word = $get_word['Listnumber'][0]['words'];
$clone = array( 'id' => '6275', 'chart' => '', 'question_id' => '38522', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Dana) places $(n3) $(boxes) an equal distance from one another. The distance between the first $(box) and the $(n3rd) $(box) is $(n150) cm. If $(Dana) adds another $(n10) $(boxes) that are equal distance apart,<br /> <ol> <li>How many gaps will there be between the $(n10th) $(box) and the $(n13th) $(box)?</li> <li>What is the distance between the $(n10)th $(box) and the $(n13)th $(box)?</li> </ol>', 'clone_solution_step' => '(a)<br />Number of gaps between $(n3) $(boxes) <br />= $(n3) - 1 <br />= $(n2) <br /> <br /> Distance between two $(boxes)<br /> = $(n150) ÷ $(n2) <br /> = $(n75) cm <br /> <br /> Number of gaps between the $(n10th) and the $(n13th) $(box)<br /> = $(n13) - $(n10) <br /> = $(n3)<br /> <br />(b)<br />Distance between the $(n10th) and the $(n13th) $(box) <br /> = $(n3) x $(n75) <br /> = $(n225) cm <br /> <br /> Answer(s): (a) $(n3); (b) $(n225) cm', 'clone_answer' => '(a) 6; (b) $(n225) cm ', 'array' => object(stdClass) { 1516845019891 => object(stdClass) {} 1516845021104 => object(stdClass) {} 1516845070706 => object(stdClass) {} 1516845080629 => object(stdClass) {} 1516845091333 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2018-01-18 16:19:37', 'modified' => '2020-06-06 21:00:47', 'original_question' => 'Dana places 3 boxes an equal distance from one another. The distance between the 1st box and the 3rd box is 150 cm. If Dana adds another 10 boxes that are equal distance apart, how many gaps will there be between the 10th box and the 13th box? What is the distance between the 10th box and the 13th box?', 'formula' => array( (int) 0 => '$(n10)+$(n3)=$(n13)', (int) 1 => '$(n150b)*10=$(n150)', (int) 2 => 'array_singular($(boxes))=$(box) ', (int) 3 => 'array_get_words(1,ordinalnumber,$(n3))=$(n3rd) ', (int) 4 => 'array_get_words(1,ordinalnumber,$(n13))=$(n13th) ', (int) 5 => 'array_get_words(1,ordinalnumber,$(n10))=$(n10th) ', (int) 6 => '$(n3) - 1 = $(n2) ', (int) 7 => '$(n150) /$(n2) = $(n75)', (int) 8 => 'if(whole_number($(n75))) continue', (int) 9 => '$(n13) - $(n10) = $(n3)', (int) 10 => '$(n3) *$(n75) = $(n225)' ), 'time_value' => array( (int) 0 => '1516845106404', (int) 1 => '1575377925193', (int) 2 => '1516845147788', (int) 3 => '1591444275914', (int) 4 => '1591444453828', (int) 5 => '1591444453365', (int) 6 => '1516845184973', (int) 7 => '1516845185154', (int) 8 => '1516845186076', (int) 9 => '1516845187069', (int) 10 => '1516845229315' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '' ), '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 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P3.WN.JC.17121100-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","",""]', 'original_solution' => '(a)<br />Number of gaps between 3 boxes = 3 - 1 = 2 <br /> <br /> Distance between two boxes <br /> = 150 ÷ 2 <br /> = 75 cm <br /> <br /> Number of gaps between the 10th and 13th box<br /> = 13 - 10 <br /> = 3<br /> <br />(b)<br /> Distance between the 10th and the 13th box <br /> = 3 x 75 <br /> = 225 cm <br /> <br /> Answer(s): 225 cm', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '21' 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 = '(a) $(n3); (b) $(n225) cm ' $count_crition = (int) 1 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 2 => 'boxes', (int) 0 => 'n10', (int) 3 => 'n3', (int) 6 => 'n3', (int) 9 => 'n10', (int) 10 => 'n3', (int) 1 => 'n150b', (int) 5 => 'n10', (int) 4 => '(n13)', (int) 7 => '(n150)' ) $tempt = array() $list_name_array = array( (int) 0 => 'Pamela', (int) 1 => 'bags' ) $list_array_item = array( 'Dana' => array( 'listArray' => array( (int) 0 => 'Xylia', (int) 1 => 'Elyse', (int) 2 => 'Gwen', (int) 3 => 'Nicole', (int) 4 => 'Penelope', (int) 5 => 'Kylie', (int) 6 => 'Ivory', (int) 7 => 'Victoria', (int) 8 => 'Shannon', (int) 9 => 'Shiyun', (int) 10 => 'Jaslyn', (int) 11 => 'Sabrina', (int) 12 => 'Joelle', (int) 13 => 'Rachel', (int) 14 => 'Jade', (int) 15 => 'Jen', (int) 16 => 'Gem', (int) 17 => 'Jean', (int) 18 => 'Barbara', (int) 19 => 'Marion', (int) 20 => 'Tiffany', (int) 21 => 'Esther', (int) 22 => 'Lucy', (int) 23 => 'Emma', (int) 24 => 'Erika', (int) 25 => 'Anna', (int) 26 => 'Betty', (int) 27 => 'Cathy', (int) 28 => 'Diana', (int) 29 => 'Eva', (int) 30 => 'Fiona', (int) 31 => 'Gillian', (int) 32 => 'Hazel', (int) 33 => 'Abi', (int) 34 => 'Cindy', (int) 35 => 'Dana', (int) 36 => 'Emily', (int) 37 => 'Fanny', (int) 38 => 'Gabby', (int) 39 => 'Hilda', (int) 40 => 'Irene', (int) 41 => 'Julie', (int) 42 => 'Jane', (int) 43 => 'Kathy', (int) 44 => 'Kimberly', (int) 45 => 'Linda', (int) 46 => 'Lynn', (int) 47 => 'Mary', (int) 48 => 'Min', (int) 49 => 'Olivia', (int) 50 => 'Opal', (int) 51 => 'Nora', (int) 52 => 'Natalie', (int) 53 => 'Pamela', (int) 54 => 'Risa', (int) 55 => 'Raeann', (int) 56 => 'Roshel', (int) 57 => 'Sarah', (int) 58 => 'Tammy', (int) 59 => 'Tina', (int) 60 => 'Usha', (int) 61 => 'Vanessa', (int) 62 => 'Winnie', (int) 63 => 'Wendy', (int) 64 => 'Xandra', (int) 65 => 'Xuan', (int) 66 => 'Yoko', (int) 67 => 'Yen', (int) 68 => 'Zara', (int) 69 => 'Zoe' ), 'keyArray' => (int) 53, 'manyArray' => '1', 'capitalize' => '0' ), 'boxes' => array( 'listArray' => array( (int) 0 => 'packets', (int) 1 => 'bags' ), 'keyArray' => (int) 1, 'manyArray' => '2', 'capitalize' => '2' ) ) $list_italic = array() $array_variable = object(stdClass) { 1516845019891 => object(stdClass) {} 1516845021104 => object(stdClass) {} 1516845070706 => object(stdClass) {} 1516845080629 => object(stdClass) {} 1516845091333 => object(stdClass) {} } $question_content = '$(Dana) places $(n3) $(boxes) an equal distance from one another. The distance between the first $(box) and the $(n3rd) $(box) is $(n150) cm. If $(Dana) adds another $(n10) $(boxes) that are equal distance apart,<br /> <ol> <li>How many gaps will there be between the $(n10th) $(box) and the $(n13th) $(box)?</li> <li>What is the distance between the $(n10)th $(box) and the $(n13)th $(box)?</li> </ol>' $solution_step = '(a)<br />Number of gaps between $(n3) $(boxes) <br />= $(n3) - 1 <br />= $(n2) <br /> <br /> Distance between two $(boxes)<br /> = $(n150) ÷ $(n2) <br /> = $(n75) cm <br /> <br /> Number of gaps between the $(n10th) and the $(n13th) $(box)<br /> = $(n13) - $(n10) <br /> = $(n3)<br /> <br />(b)<br />Distance between the $(n10th) and the $(n13th) $(box) <br /> = $(n3) x $(n75) <br /> = $(n225) cm <br /> <br /> Answer(s): (a) $(n3); (b) $(n225) cm' $clone_answer = '(a) $(n3); (b) $(n225) cm ' $formula = array( (int) 0 => '15+6=21', (int) 1 => '14*10=140', (int) 2 => 'array_singular(bags)=bag', (int) 3 => 'array_get_words(1,ordinalnumber,6)=sixth', (int) 4 => 'array_get_words(1,ordinalnumber,21)=$(n13th)', (int) 5 => 'array_get_words(1,ordinalnumber,15)=$(n10th)', (int) 6 => '6-1=$(n2)', (int) 7 => '140/$(n2)=$(n75)', (int) 8 => 'if(whole_number($(n75)))continue', (int) 9 => '21-15=6', (int) 10 => '6*$(n75)=$(n225)' ) $formula_1 = array( (int) 0 => '$(n10)+$(n3)=$(n13)', (int) 1 => '$(n150b)*10=$(n150)', (int) 2 => 'array_singular($(boxes))=$(box) ', (int) 3 => 'array_get_words(1,ordinalnumber,$(n3))=$(n3rd) ', (int) 4 => 'array_get_words(1,ordinalnumber,$(n13))=$(n13th) ', (int) 5 => 'array_get_words(1,ordinalnumber,$(n10))=$(n10th) ', (int) 6 => '$(n3) - 1 = $(n2) ', (int) 7 => '$(n150) /$(n2) = $(n75)', (int) 8 => 'if(whole_number($(n75))) continue', (int) 9 => '$(n13) - $(n10) = $(n3)', (int) 10 => '$(n3) *$(n75) = $(n225)' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '' ) $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 => '' ) $time_value = array( (int) 0 => '1516845106404', (int) 1 => '1575377925193', (int) 2 => '1516845147788', (int) 3 => '1591444275914', (int) 4 => '1591444453828', (int) 5 => '1591444453365', (int) 6 => '1516845184973', (int) 7 => '1516845185154', (int) 8 => '1516845186076', (int) 9 => '1516845187069', (int) 10 => '1516845229315' ) $k = '1516845091333' $v = object(stdClass) { cate => 'whole_number' name => 'n10' range => object(stdClass) {} attr => object(stdClass) {} } $array_system = array( (int) 0 => 'packets', (int) 1 => 'bags' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 1 $value_check = 'bags' $check_who_nnt = (int) 0 $from = '10' $to = '15' $arr_variable = array( 'Dana' => 'Pamela', 'boxes' => 'bags', 'n3' => (int) 6, 'n150b' => (int) 14, 'n10' => (int) 15, '(n13)' => (int) 21, '(n150)' => (int) 140, '(box)' => 'bag', '(n3rd)' => 'sixth' ) $variable_k = '(n3rd)' $variable_v = 'sixth' $formula_k = (int) 4 $formula_v = 'array_get_words(1,ordinalnumber,$(n13))=$(n13th)' $criterion_k = (int) 10 $criterion_v = '' $type_criterion_k = (int) 10 $type_criterion_v = '' $variable_show = array( 'Dana' => 'Pamela', 'boxes' => 'bags', 'n3' => (int) 6, 'n150b' => (int) 14, 'n10' => (int) 15 ) $start = 'array_get_words(' $end = ')' $array_mixed_nnt = array() $check_changes = '6*$(n75)=$(n225)' $criterion_continue = '$(n13th)' $criterion_back = '3th)' $get_between = array( (int) 0 => '1', (int) 1 => 'ordinalnumber', (int) 2 => '21' ) $bieuthuc = array( (int) 0 => 'array_get_words(1,ordinalnumber,21)', (int) 1 => '(n13th)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = 'sixth' $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 $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' => '4', 'name' => 'ordinalnumber', 'name_check' => 'ordinalnumber', 'created' => '2017-09-11 11:50:48', 'modified' => '2017-12-07 15:27:34' ), 'Listnumber' => array() ) $array_get_word = 'sixth' $k1 = (int) 10 $v1 = '6*$(n75)=$(n225)'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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Date:26 Jun 2024
Topic:WHOLE NUMBERS
Question Number:P3.WN.JC.17121100-A1
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