Archie has 7 more 10-cent coins than 5-cent coins. After he used 8 of his 10-cent coins, the total value of 10-cent coins is $1.60 more than the total value of 5-cent coins. How many coins did he have at first?
| |
10¢ |
5¢ |
| Before |
1 u + 7 |
1 u |
| Change |
- 8 |
|
| 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¢
$1.60 = 160¢
Number of 10¢ coins in the end
= 1 u + 7 - 8
= 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 8 10-cent coins, the value of 10-cent coins is 160¢ more than the value of 5-cent coins. If another 160¢ 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 + 160
10 u - 5 u = 160 + 10
5 u = 170
1 u = 170 ÷ 5 = 34
Number of coins that Archie had at first
= 1 u + 1 u + 7
= 2 u + 7
= (2 x 34) + 7
= 68 + 7
= 75
Answer(s): 75
