Fred has 6 more 50-cent coins than 20-cent coins. After he used 18 of his 50-cent coins, the total value of 50-cent coins is $3.60 more than the total value of 20-cent coins. How many coins did he have in the end?
|
50¢ |
20¢ |
Before |
1 u + 6 |
1 u |
Change |
- 18 |
|
After |
1 u - 12 |
1 u |
|
50¢ |
20¢ |
Number |
1 u - 12 |
1 u |
Value |
50 |
20 |
Total value |
50 u - 600 |
20 u |
$1 = 100¢
$3.60 = 360¢
Number of 50¢ coins in the end
= 1 u + 6 - 18
= 1 u - 12
Total value of 50¢ coins in the end
= 50 x (1 u - 12)
= 50 u - 600
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 18 50-cent coins, the value of 50-cent coins is 360¢ more than the value of 20-cent coins. If another 360¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 600 = 20 u + 360
50 u - 20 u = 360 + 600
30 u = 960
1 u = 960 ÷ 30 = 32
Number of coins that Fred had in the end
= 1 u + 1 u - 12
= 2 u - 12
= (2 x 32) - 12
= 64 - 12
= 52
Answer(s): 52