Sam started saving part of his pocket money by putting 2 coins in a money box every day. Each coin was either a 10¢ or 20¢ coin. His grandfather also put on a $1 coin in the box every 7 days. The total value of the coins after 77 days was $32.60.
- How many coins were there altogether?
- How many of the coins were 20¢ coins?
Total nuber of coins that his grandfather put in
= 77 ÷ 7
= 11
Total number of coins that Sam saved
= 2 x 77 = 154 Total number of coins
= 11 + 154
= 165
(b)
Amount contributed by his grandfather
= 11 x 1
= $11
Amount that Sam saved
= 32.60 - 11
= $21.60
$1 = 100¢
$21.60 = 2160¢
Number of 20¢ coins |
Total value of 20¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
154
|
154 x 20 = 3080¢ |
0
|
0
|
3080¢
|
153
|
153 x 20 = 3060¢ |
1
|
1 x 10 = 10¢ |
3070¢
|
62 |
62 x 20 = 1240¢ |
92 |
92 x 10 = 920¢ |
2160¢
|
Amount that Sam saved if all he saved were 20¢ coins
= 154 x 20
= 3080
Big difference between the total values of 20¢ coins and 10¢ coins
= 3080 - 2160
= 920
Small difference between the value of 20¢ coins and 10¢ coins
= 20 - 10
= 10
Number of 10¢ coins
= 920 ÷ 10
= 92
Number of 20¢ coins
= 154 - 92
= 62
Answer(s): (a) 165; (b) 62