George has 4 more 10-cent coins than 5-cent coins. After he used 5 of his 10-cent coins, the total value of 10-cent coins is $2.60 more than the total value of 5-cent coins. How many coins did he have at first?
| |
10¢ |
5¢ |
| Before |
1 u + 4 |
1 u |
| Change |
- 5 |
|
| After |
1 u - 1 |
1 u |
| |
10¢ |
5¢ |
| Number |
1 u - 1 |
1 u |
| Value |
10 |
5 |
| Total value |
10 u - 10 |
5 u |
$1 = 100¢
$2.60 = 260¢
Number of 10¢ coins in the end
= 1 u + 4 - 5
= 1 u - 1
Total value of 10¢ coins in the end
= 10 x (1 u - 1)
= 10 u - 10
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 5 10-cent coins, the value of 10-cent coins is 260¢ more than the value of 5-cent coins. If another 260¢ is added to the 5-cent coins, the total value of 10-cent coins and 5-cent coins will be the same.
10 u - 10 = 5 u + 260
10 u - 5 u = 260 + 10
5 u = 270
1 u = 270 ÷ 5 = 54
Number of coins that George had at first
= 1 u + 1 u + 4
= 2 u + 4
= (2 x 54) + 4
= 108 + 4
= 112
Answer(s): 112
