Ethan has 3 more 20-cent coins than 5-cent coins. After he used 12 of his 20-cent coins, the total value of 20-cent coins is $1.20 more than the total value of 5-cent coins. How many coins did he have in the end?
| |
20¢ |
5¢ |
| Before |
1 u + 3 |
1 u |
| Change |
- 12 |
|
| After |
1 u - 9 |
1 u |
| |
20¢ |
5¢ |
| Number |
1 u - 9 |
1 u |
| Value |
20 |
5 |
| Total value |
20 u - 180 |
5 u |
$1 = 100¢
$1.20 = 120¢
Number of 20¢ coins in the end
= 1 u + 3 - 12
= 1 u - 9
Total value of 20¢ coins in the end
= 20 x (1 u - 9)
= 20 u - 180
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 12 20-cent coins, the value of 20-cent coins is 120¢ more than the value of 5-cent coins. If another 120¢ is added to the 5-cent coins, the total value of 20-cent coins and 5-cent coins will be the same.
20 u - 180 = 5 u + 120
20 u - 5 u = 120 + 180
15 u = 300
1 u = 300 ÷ 15 = 20
Number of coins that Ethan had in the end
= 1 u + 1 u - 9
= 2 u - 9
= (2 x 20) - 9
= 40 - 9
= 31
Answer(s): 31
