Will 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 father also put on a $1 coin in the box every 7 days. The total value of the coins after 70 days was $57.50.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his father put in
= 70 ÷ 7
= 10
Total number of coins that Will saved
= 2 x 70 = 140 Total number of coins
= 10 + 140
= 150
(b)
Amount contributed by his father
= 10 x 1
= $10
Amount that Will saved
= 57.50 - 10
= $47.50
$1 = 100¢
$47.50 = 4750¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
140
|
140 x 50 = 7000¢ |
0
|
0
|
7000¢
|
139
|
139 x 50 = 6950¢ |
1
|
1 x 20 = 20¢ |
6970¢
|
65 |
65 x 50 = 3250¢ |
75 |
75 x 20 = 1500¢ |
4750¢
|
Amount that Will saved if all he saved were 50¢ coins
= 140 x 50
= 7000
Big difference between the total values of 50¢ coins and 20¢ coins
= 7000 - 4750
= 2250
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 2250 ÷ 30
= 75
Number of 50¢ coins
= 140 - 75
= 65
Answer(s): (a) 150; (b) 65