Oscar has 2 more 10-cent coins than 5-cent coins. After he used 3 of his 10-cent coins, the total value of 10-cent coins is $4.10 more than the total value of 5-cent coins. How many coins did he have in the end?
| |
10¢ |
5¢ |
| Before |
1 u + 2 |
1 u |
| Change |
- 3 |
|
| 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¢
$4.10 = 410¢
Number of 10¢ coins in the end
= 1 u + 2 - 3
= 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 3 10-cent coins, the value of 10-cent coins is 410¢ more than the value of 5-cent coins. If another 410¢ 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 + 410
10 u - 5 u = 410 + 10
5 u = 420
1 u = 420 ÷ 5 = 84
Number of coins that Oscar had in the end
= 1 u + 1 u - 1
= 2 u - 1
= (2 x 84) - 1
= 168 - 1
= 167
Answer(s): 167
