Ethan 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 $3.50 more than the total value of 5-cent coins. How many coins did he have in the end?
|
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¢
$3.50 = 350¢
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 350¢ more than the value of 5-cent coins. If another 350¢ 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 + 350
10 u - 5 u = 350 + 30
5 u = 380
1 u = 380 ÷ 5 = 76
Number of coins that Ethan had in the end
= 1 u + 1 u - 3
= 2 u - 3
= (2 x 76) - 3
= 152 - 3
= 149
Answer(s): 149