Mark has 9 more 50-cent coins than 5-cent coins. After he used 11 of his 50-cent coins, the total value of 50-cent coins is $4.40 more than the total value of 5-cent coins. How many coins did he have in the end?
|
50¢ |
5¢ |
Before |
1 u + 9 |
1 u |
Change |
- 11 |
|
After |
1 u - 2 |
1 u |
|
50¢ |
5¢ |
Number |
1 u - 2 |
1 u |
Value |
50 |
5 |
Total value |
50 u - 100 |
5 u |
$1 = 100¢
$4.40 = 440¢
Number of 50¢ coins in the end
= 1 u + 9 - 11
= 1 u - 2
Total value of 50¢ coins in the end
= 50 x (1 u - 2)
= 50 u - 100
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 11 50-cent coins, the value of 50-cent coins is 440¢ more than the value of 5-cent coins. If another 440¢ is added to the 5-cent coins, the total value of 50-cent coins and 5-cent coins will be the same.
50 u - 100 = 5 u + 440
50 u - 5 u = 440 + 100
45 u = 540
1 u = 540 ÷ 45 = 12
Number of coins that Mark had in the end
= 1 u + 1 u - 2
= 2 u - 2
= (2 x 12) - 2
= 24 - 2
= 22
Answer(s): 22