Fabian has 8 more 50-cent coins than 20-cent coins. After he used 9 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 in the end?
|
50¢ |
20¢ |
Before |
1 u + 8 |
1 u |
Change |
- 9 |
|
After |
1 u - 1 |
1 u |
|
50¢ |
20¢ |
Number |
1 u - 1 |
1 u |
Value |
50 |
20 |
Total value |
50 u - 50 |
20 u |
$1 = 100¢
$4.30 = 430¢
Number of 50¢ coins in the end
= 1 u + 8 - 9
= 1 u - 1
Total value of 50¢ coins in the end
= 50 x (1 u - 1)
= 50 u - 50
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 9 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 - 50 = 20 u + 430
50 u - 20 u = 430 + 50
30 u = 480
1 u = 480 ÷ 30 = 16
Number of coins that Fabian had in the end
= 1 u + 1 u - 1
= 2 u - 1
= (2 x 16) - 1
= 32 - 1
= 31
Answer(s): 31