Ethan 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 63 days was $29.60.
- How many coins were there altogether?
- How many of the coins were 20¢ coins?
Total nuber of coins that his grandmother put in
= 63 ÷ 7
= 9
Total number of coins that Ethan saved
= 2 x 63 = 126 Total number of coins
= 9 + 126
= 135
(b)
Amount contributed by his grandmother
= 9 x 1
= $9
Amount that Ethan saved
= 29.60 - 9
= $20.60
$1 = 100¢
$20.60 = 2060¢
Number of 20¢ coins |
Total value of 20¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
126
|
126 x 20 = 2520¢ |
0
|
0
|
2520¢
|
125
|
125 x 20 = 2500¢ |
1
|
1 x 10 = 10¢ |
2510¢
|
80 |
80 x 20 = 1600¢ |
46 |
46 x 10 = 460¢ |
2060¢
|
Amount that Ethan saved if all he saved were 20¢ coins
= 126 x 20
= 2520
Big difference between the total values of 20¢ coins and 10¢ coins
= 2520 - 2060
= 460
Small difference between the value of 20¢ coins and 10¢ coins
= 20 - 10
= 10
Number of 10¢ coins
= 460 ÷ 10
= 46
Number of 20¢ coins
= 126 - 46
= 80
Answer(s): (a) 135; (b) 80