Reggie has 6 more 10-cent coins than 5-cent coins. After he used 12 of his 10-cent coins, the total value of 10-cent coins is $2.70 more than the total value of 5-cent coins. How many coins did he have at first?
| |
10¢ |
5¢ |
| Before |
1 u + 6 |
1 u |
| Change |
- 12 |
|
| After |
1 u - 6 |
1 u |
| |
10¢ |
5¢ |
| Number |
1 u - 6 |
1 u |
| Value |
10 |
5 |
| Total value |
10 u - 60 |
5 u |
$1 = 100¢
$2.70 = 270¢
Number of 10¢ coins in the end
= 1 u + 6 - 12
= 1 u - 6
Total value of 10¢ coins in the end
= 10 x (1 u - 6)
= 10 u - 60
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 12 10-cent coins, the value of 10-cent coins is 270¢ more than the value of 5-cent coins. If another 270¢ is added to the 5-cent coins, the total value of 10-cent coins and 5-cent coins will be the same.
10 u - 60 = 5 u + 270
10 u - 5 u = 270 + 60
5 u = 330
1 u = 330 ÷ 5 = 66
Number of coins that Reggie had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 66) + 6
= 132 + 6
= 138
Answer(s): 138
