Luke has 6 more 10-cent coins than 5-cent coins. After he used 9 of his 10-cent coins, the total value of 10-cent coins is $2.40 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 |
- 9 |
|
| After |
1 u - 3 |
1 u |
| |
10¢ |
5¢ |
| Number |
1 u - 3 |
1 u |
| Value |
10 |
5 |
| Total value |
10 u - 30 |
5 u |
$1 = 100¢
$2.40 = 240¢
Number of 10¢ coins in the end
= 1 u + 6 - 9
= 1 u - 3
Total value of 10¢ coins in the end
= 10 x (1 u - 3)
= 10 u - 30
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 9 10-cent coins, the value of 10-cent coins is 240¢ more than the value of 5-cent coins. If another 240¢ is added to the 5-cent coins, the total value of 10-cent coins and 5-cent coins will be the same.
10 u - 30 = 5 u + 240
10 u - 5 u = 240 + 30
5 u = 270
1 u = 270 ÷ 5 = 54
Number of coins that Luke had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 54) + 6
= 108 + 6
= 114
Answer(s): 114
