Billy has 6 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 $4.30 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 |
- 16 |
|
After |
1 u - 10 |
1 u |
|
50¢ |
20¢ |
Number |
1 u - 10 |
1 u |
Value |
50 |
20 |
Total value |
50 u - 500 |
20 u |
$1 = 100¢
$4.30 = 430¢
Number of 50¢ coins in the end
= 1 u + 6 - 16
= 1 u - 10
Total value of 50¢ coins in the end
= 50 x (1 u - 10)
= 50 u - 500
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 430¢ more than the value of 20-cent coins. If another 430¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 500 = 20 u + 430
50 u - 20 u = 430 + 500
30 u = 930
1 u = 930 ÷ 30 = 31
Number of coins that Billy had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 31) + 6
= 62 + 6
= 68
Answer(s): 68