Jack has 4 more 50-cent coins than 10-cent coins. After he used 8 of his 50-cent coins, the total value of 50-cent coins is $1.20 more than the total value of 10-cent coins. How many coins did he have at first?
| |
50¢ |
10¢ |
| Before |
1 u + 4 |
1 u |
| Change |
- 8 |
|
| After |
1 u - 4 |
1 u |
| |
50¢ |
10¢ |
| Number |
1 u - 4 |
1 u |
| Value |
50 |
10 |
| Total value |
50 u - 200 |
10 u |
$1 = 100¢
$1.20 = 120¢
Number of 50¢ coins in the end
= 1 u + 4 - 8
= 1 u - 4
Total value of 50¢ coins in the end
= 50 x (1 u - 4)
= 50 u - 200
Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u
After using 8 50-cent coins, the value of 50-cent coins is 120¢ more than the value of 10-cent coins. If another 120¢ is added to the 10-cent coins, the total value of 50-cent coins and 10-cent coins will be the same.
50 u - 200 = 10 u + 120
50 u - 10 u = 120 + 200
40 u = 320
1 u = 320 ÷ 40 = 8
Number of coins that Jack had at first
= 1 u + 1 u + 4
= 2 u + 4
= (2 x 8) + 4
= 16 + 4
= 20
Answer(s): 20
