Peter started saving part of his pocket money by putting 2 coins in a money box every day. Each coin was either a 20¢ or 50¢ coin. His mother also put on a $1 coin in the box every 7 days. The total value of the coins after 63 days was $59.10.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his mother put in
= 63 ÷ 7
= 9
Total number of coins that Peter saved
= 2 x 63 = 126 Total number of coins
= 9 + 126
= 135
(b)
Amount contributed by his mother
= 9 x 1
= $9
Amount that Peter saved
= 59.10 - 9
= $50.10
$1 = 100¢
$50.10 = 5010¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
126
|
126 x 50 = 6300¢ |
0
|
0
|
6300¢
|
125
|
125 x 50 = 6250¢ |
1
|
1 x 20 = 20¢ |
6270¢
|
83 |
83 x 50 = 4150¢ |
43 |
43 x 20 = 860¢ |
5010¢
|
Amount that Peter saved if all he saved were 50¢ coins
= 126 x 50
= 6300
Big difference between the total values of 50¢ coins and 20¢ coins
= 6300 - 5010
= 1290
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 1290 ÷ 30
= 43
Number of 50¢ coins
= 126 - 43
= 83
Answer(s): (a) 135; (b) 83