Billy has 9 more 50-cent coins than 20-cent coins. After he used 12 of his 50-cent coins, the total value of 50-cent coins is $4.50 more than the total value of 20-cent coins. How many coins did he have in the end?
|
50¢ |
20¢ |
Before |
1 u + 9 |
1 u |
Change |
- 12 |
|
After |
1 u - 3 |
1 u |
|
50¢ |
20¢ |
Number |
1 u - 3 |
1 u |
Value |
50 |
20 |
Total value |
50 u - 150 |
20 u |
$1 = 100¢
$4.50 = 450¢
Number of 50¢ coins in the end
= 1 u + 9 - 12
= 1 u - 3
Total value of 50¢ coins in the end
= 50 x (1 u - 3)
= 50 u - 150
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 12 50-cent coins, the value of 50-cent coins is 450¢ more than the value of 20-cent coins. If another 450¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 150 = 20 u + 450
50 u - 20 u = 450 + 150
30 u = 600
1 u = 600 ÷ 30 = 20
Number of coins that Billy had in the end
= 1 u + 1 u - 3
= 2 u - 3
= (2 x 20) - 3
= 40 - 3
= 37
Answer(s): 37