Ben 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 father also put on a $1 coin in the box every 7 days. The total value of the coins after 63 days was $42.80.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his father put in
= 63 ÷ 7
= 9
Total number of coins that Ben saved
= 2 x 63 = 126 Total number of coins
= 9 + 126
= 135
(b)
Amount contributed by his father
= 9 x 1
= $9
Amount that Ben saved
= 42.80 - 9
= $33.80
$1 = 100¢
$33.80 = 3380¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
126
|
126 x 50 = 6300¢ |
0
|
0
|
6300¢
|
125
|
125 x 50 = 6250¢ |
1
|
1 x 10 = 10¢ |
6260¢
|
53 |
53 x 50 = 2650¢ |
73 |
73 x 10 = 730¢ |
3380¢
|
Amount that Ben saved if all he saved were 50¢ coins
= 126 x 50
= 6300
Big difference between the total values of 50¢ coins and 10¢ coins
= 6300 - 3380
= 2920
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 2920 ÷ 40
= 73
Number of 50¢ coins
= 126 - 73
= 53
Answer(s): (a) 135; (b) 53