Tom 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 grandmother also put on a $1 coin in the box every 7 days. The total value of the coins after 70 days was $29.70.
- How many coins were there altogether?
- How many of the coins were 20¢ coins?
Total nuber of coins that his grandmother put in
= 70 ÷ 7
= 10
Total number of coins that Tom saved
= 2 x 70 = 140 Total number of coins
= 10 + 140
= 150
(b)
Amount contributed by his grandmother
= 10 x 1
= $10
Amount that Tom saved
= 29.70 - 10
= $19.70
$1 = 100¢
$19.70 = 1970¢
Number of 20¢ coins |
Total value of 20¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
140
|
140 x 20 = 2800¢ |
0
|
0
|
2800¢
|
139
|
139 x 20 = 2780¢ |
1
|
1 x 10 = 10¢ |
2790¢
|
57 |
57 x 20 = 1140¢ |
83 |
83 x 10 = 830¢ |
1970¢
|
Amount that Tom saved if all he saved were 20¢ coins
= 140 x 20
= 2800
Big difference between the total values of 20¢ coins and 10¢ coins
= 2800 - 1970
= 830
Small difference between the value of 20¢ coins and 10¢ coins
= 20 - 10
= 10
Number of 10¢ coins
= 830 ÷ 10
= 83
Number of 20¢ coins
= 140 - 83
= 57
Answer(s): (a) 150; (b) 57