Luke has 6 more 50-cent coins than 20-cent coins. After he used 13 of his 50-cent coins, the total value of 50-cent coins is $3.10 more than the total value of 20-cent coins. How many coins did he have at first?
| |
50¢ |
20¢ |
| Before |
1 u + 6 |
1 u |
| Change |
- 13 |
|
| After |
1 u - 7 |
1 u |
| |
50¢ |
20¢ |
| Number |
1 u - 7 |
1 u |
| Value |
50 |
20 |
| Total value |
50 u - 350 |
20 u |
$1 = 100¢
$3.10 = 310¢
Number of 50¢ coins in the end
= 1 u + 6 - 13
= 1 u - 7
Total value of 50¢ coins in the end
= 50 x (1 u - 7)
= 50 u - 350
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 13 50-cent coins, the value of 50-cent coins is 310¢ more than the value of 20-cent coins. If another 310¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 350 = 20 u + 310
50 u - 20 u = 310 + 350
30 u = 660
1 u = 660 ÷ 30 = 22
Number of coins that Luke had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 22) + 6
= 44 + 6
= 50
Answer(s): 50
