Liam 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 grandfather also put on a $1 coin in the box every 7 days. The total value of the coins after 42 days was $44.80.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his grandfather put in
= 42 ÷ 7
= 6
Total number of coins that Liam saved
= 2 x 42 = 84 Total number of coins
= 6 + 84
= 90
(b)
Amount contributed by his grandfather
= 6 x 1
= $6
Amount that Liam saved
= 44.80 - 6
= $38.80
$1 = 100¢
$38.80 = 3880¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
84
|
84 x 50 = 4200¢ |
0
|
0
|
4200¢
|
83
|
83 x 50 = 4150¢ |
1
|
1 x 10 = 10¢ |
4160¢
|
76 |
76 x 50 = 3800¢ |
8 |
8 x 10 = 80¢ |
3880¢
|
Amount that Liam saved if all he saved were 50¢ coins
= 84 x 50
= 4200
Big difference between the total values of 50¢ coins and 10¢ coins
= 4200 - 3880
= 320
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 320 ÷ 40
= 8
Number of 50¢ coins
= 84 - 8
= 76
Answer(s): (a) 90; (b) 76