Michael has 4 more 50-cent coins than 5-cent coins. After he used 14 of his 50-cent coins, the total value of 50-cent coins is $3.10 more than the total value of 5-cent coins. How many coins did he have at first?

	50¢	5¢
Before	1 u + 4	1 u
Change	- 14
After	1 u - 10	1 u

	50¢	5¢
Number	1 u - 10	1 u
Value	50	5
Total value	50 u - 500	5 u

$1 = 100¢
$3.10 = 310¢

Number of 50¢ coins in the end
= 1 u + 4 - 14
= 1 u - 10

Total value of 50¢ coins in the end
= 50 x (1 u - 10)
= 50 u - 500

Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u

After using 14 50-cent coins, the value of 50-cent coins is 310¢ more than the value of 5-cent coins. If another 310¢ is added to the 5-cent coins, the total value of 50-cent coins and 5-cent coins will be the same.

50 u - 500 = 5 u + 310
50 u - 5 u = 310 + 500
45 u = 810

1 u = 810 ÷ 45 = 18

Number of coins that Michael had at first
= 1 u + 1 u + 4
= 2 u + 4
= (2 x 18) + 4
= 36 + 4
= 40

Answer(s): 40