Valen has 7 more 50-cent coins than 10-cent coins. After he used 12 of his 50-cent coins, the total value of 50-cent coins is $1.90 more than the total value of 10-cent coins. How many coins did he have at first?
| |
50¢ |
10¢ |
| Before |
1 u + 7 |
1 u |
| Change |
- 12 |
|
| After |
1 u - 5 |
1 u |
| |
50¢ |
10¢ |
| Number |
1 u - 5 |
1 u |
| Value |
50 |
10 |
| Total value |
50 u - 250 |
10 u |
$1 = 100¢
$1.90 = 190¢
Number of 50¢ coins in the end
= 1 u + 7 - 12
= 1 u - 5
Total value of 50¢ coins in the end
= 50 x (1 u - 5)
= 50 u - 250
Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u
After using 12 50-cent coins, the value of 50-cent coins is 190¢ more than the value of 10-cent coins. If another 190¢ is added to the 10-cent coins, the total value of 50-cent coins and 10-cent coins will be the same.
50 u - 250 = 10 u + 190
50 u - 10 u = 190 + 250
40 u = 440
1 u = 440 ÷ 40 = 11
Number of coins that Valen had at first
= 1 u + 1 u + 7
= 2 u + 7
= (2 x 11) + 7
= 22 + 7
= 29
Answer(s): 29
