Tom 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 grandmother also put on a $1 coin in the box every 7 days. The total value of the coins after 77 days was $62.50.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his grandmother put in
= 77 ÷ 7
= 11
Total number of coins that Tom saved
= 2 x 77 = 154 Total number of coins
= 11 + 154
= 165
(b)
Amount contributed by his grandmother
= 11 x 1
= $11
Amount that Tom saved
= 62.50 - 11
= $51.50
$1 = 100¢
$51.50 = 5150¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
154
|
154 x 50 = 7700¢ |
0
|
0
|
7700¢
|
153
|
153 x 50 = 7650¢ |
1
|
1 x 20 = 20¢ |
7670¢
|
69 |
69 x 50 = 3450¢ |
85 |
85 x 20 = 1700¢ |
5150¢
|
Amount that Tom saved if all he saved were 50¢ coins
= 154 x 50
= 7700
Big difference between the total values of 50¢ coins and 20¢ coins
= 7700 - 5150
= 2550
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 2550 ÷ 30
= 85
Number of 50¢ coins
= 154 - 85
= 69
Answer(s): (a) 165; (b) 69