Albert 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 grandmother also put on a $1 coin in the box every 7 days. The total value of the coins after 56 days was $45.60.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his grandmother put in
= 56 ÷ 7
= 8
Total number of coins that Albert saved
= 2 x 56 = 112 Total number of coins
= 8 + 112
= 120
(b)
Amount contributed by his grandmother
= 8 x 1
= $8
Amount that Albert saved
= 45.60 - 8
= $37.60
$1 = 100¢
$37.60 = 3760¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
112
|
112 x 50 = 5600¢ |
0
|
0
|
5600¢
|
111
|
111 x 50 = 5550¢ |
1
|
1 x 10 = 10¢ |
5560¢
|
66 |
66 x 50 = 3300¢ |
46 |
46 x 10 = 460¢ |
3760¢
|
Amount that Albert saved if all he saved were 50¢ coins
= 112 x 50
= 5600
Big difference between the total values of 50¢ coins and 10¢ coins
= 5600 - 3760
= 1840
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 1840 ÷ 40
= 46
Number of 50¢ coins
= 112 - 46
= 66
Answer(s): (a) 120; (b) 66