Ethan has 3 more 10-cent coins than 5-cent coins. After he used 14 of his 10-cent coins, the total value of 10-cent coins is $2.10 more than the total value of 5-cent coins. How many coins did he have in the end?
|
10¢ |
5¢ |
Before |
1 u + 3 |
1 u |
Change |
- 14 |
|
After |
1 u - 11 |
1 u |
|
10¢ |
5¢ |
Number |
1 u - 11 |
1 u |
Value |
10 |
5 |
Total value |
10 u - 110 |
5 u |
$1 = 100¢
$2.10 = 210¢
Number of 10¢ coins in the end
= 1 u + 3 - 14
= 1 u - 11
Total value of 10¢ coins in the end
= 10 x (1 u - 11)
= 10 u - 110
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 14 10-cent coins, the value of 10-cent coins is 210¢ more than the value of 5-cent coins. If another 210¢ is added to the 5-cent coins, the total value of 10-cent coins and 5-cent coins will be the same.
10 u - 110 = 5 u + 210
10 u - 5 u = 210 + 110
5 u = 320
1 u = 320 ÷ 5 = 64
Number of coins that Ethan had in the end
= 1 u + 1 u - 11
= 2 u - 11
= (2 x 64) - 11
= 128 - 11
= 117
Answer(s): 117