Luis has 5 more 50-cent coins than 20-cent coins. After he used 16 of his 50-cent coins, the total value of 50-cent coins is $4.10 more than the total value of 20-cent coins. How many coins did he have at first?
| |
50¢ |
20¢ |
| Before |
1 u + 5 |
1 u |
| Change |
- 16 |
|
| After |
1 u - 11 |
1 u |
| |
50¢ |
20¢ |
| Number |
1 u - 11 |
1 u |
| Value |
50 |
20 |
| Total value |
50 u - 550 |
20 u |
$1 = 100¢
$4.10 = 410¢
Number of 50¢ coins in the end
= 1 u + 5 - 16
= 1 u - 11
Total value of 50¢ coins in the end
= 50 x (1 u - 11)
= 50 u - 550
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 16 50-cent coins, the value of 50-cent coins is 410¢ more than the value of 20-cent coins. If another 410¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 550 = 20 u + 410
50 u - 20 u = 410 + 550
30 u = 960
1 u = 960 ÷ 30 = 32
Number of coins that Luis had at first
= 1 u + 1 u + 5
= 2 u + 5
= (2 x 32) + 5
= 64 + 5
= 69
Answer(s): 69
