Sean started saving part of his pocket money by putting 2 coins in a money box every day. Each coin was either a 10¢ or 50¢ coin. His mother also put on a $1 coin in the box every 7 days. The total value of the coins after 91 days was $57.60.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his mother put in
= 91 ÷ 7
= 13
Total number of coins that Sean saved
= 2 x 91 = 182 Total number of coins
= 13 + 182
= 195
(b)
Amount contributed by his mother
= 13 x 1
= $13
Amount that Sean saved
= 57.60 - 13
= $44.60
$1 = 100¢
$44.60 = 4460¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
182
|
182 x 50 = 9100¢ |
0
|
0
|
9100¢
|
181
|
181 x 50 = 9050¢ |
1
|
1 x 10 = 10¢ |
9060¢
|
66 |
66 x 50 = 3300¢ |
116 |
116 x 10 = 1160¢ |
4460¢
|
Amount that Sean saved if all he saved were 50¢ coins
= 182 x 50
= 9100
Big difference between the total values of 50¢ coins and 10¢ coins
= 9100 - 4460
= 4640
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 4640 ÷ 40
= 116
Number of 50¢ coins
= 182 - 116
= 66
Answer(s): (a) 195; (b) 66