Caden has 9 more 20-cent coins than 5-cent coins. After he used 17 of his 20-cent coins, the total value of 20-cent coins is $3.20 more than the total value of 5-cent coins. How many coins did he have at first?
| |
20¢ |
5¢ |
| Before |
1 u + 9 |
1 u |
| Change |
- 17 |
|
| After |
1 u - 8 |
1 u |
| |
20¢ |
5¢ |
| Number |
1 u - 8 |
1 u |
| Value |
20 |
5 |
| Total value |
20 u - 160 |
5 u |
$1 = 100¢
$3.20 = 320¢
Number of 20¢ coins in the end
= 1 u + 9 - 17
= 1 u - 8
Total value of 20¢ coins in the end
= 20 x (1 u - 8)
= 20 u - 160
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 17 20-cent coins, the value of 20-cent coins is 320¢ more than the value of 5-cent coins. If another 320¢ is added to the 5-cent coins, the total value of 20-cent coins and 5-cent coins will be the same.
20 u - 160 = 5 u + 320
20 u - 5 u = 320 + 160
15 u = 480
1 u = 480 ÷ 15 = 32
Number of coins that Caden had at first
= 1 u + 1 u + 9
= 2 u + 9
= (2 x 32) + 9
= 64 + 9
= 73
Answer(s): 73
