Glen has 9 more 10-cent coins than 5-cent coins. After he used 19 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 + 9 |
1 u |
Change |
- 19 |
|
After |
1 u - 10 |
1 u |
|
10¢ |
5¢ |
Number |
1 u - 10 |
1 u |
Value |
10 |
5 |
Total value |
10 u - 100 |
5 u |
$1 = 100¢
$1.60 = 160¢
Number of 10¢ coins in the end
= 1 u + 9 - 19
= 1 u - 10
Total value of 10¢ coins in the end
= 10 x (1 u - 10)
= 10 u - 100
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 19 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 - 100 = 5 u + 160
10 u - 5 u = 160 + 100
5 u = 260
1 u = 260 ÷ 5 = 52
Number of coins that Glen had at first
= 1 u + 1 u + 9
= 2 u + 9
= (2 x 52) + 9
= 104 + 9
= 113
Answer(s): 113