Fred has 4 more 50-cent coins than 10-cent coins. After he used 19 of his 50-cent coins, the total value of 50-cent coins is $2.90 more than the total value of 10-cent coins. How many coins did he have at first?

	50¢	10¢
Before	1 u + 4	1 u
Change	- 19
After	1 u - 15	1 u

	50¢	10¢
Number	1 u - 15	1 u
Value	50	10
Total value	50 u - 750	10 u

$1 = 100¢
$2.90 = 290¢

Number of 50¢ coins in the end
= 1 u + 4 - 19
= 1 u - 15

Total value of 50¢ coins in the end
= 50 x (1 u - 15)
= 50 u - 750

Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u

After using 19 50-cent coins, the value of 50-cent coins is 290¢ more than the value of 10-cent coins. If another 290¢ is added to the 10-cent coins, the total value of 50-cent coins and 10-cent coins will be the same.

50 u - 750 = 10 u + 290
50 u - 10 u = 290 + 750
40 u = 1040

1 u = 1040 ÷ 40 = 26

Number of coins that Fred had at first
= 1 u + 1 u + 4
= 2 u + 4
= (2 x 26) + 4
= 52 + 4
= 56

Answer(s): 56