Valen has 4 more 50-cent coins than 10-cent coins. After he used 14 of his 50-cent coins, the total value of 50-cent coins is $1.80 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	- 14
After	1 u - 10	1 u

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

$1 = 100¢
$1.80 = 180¢

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 10¢ coins in the end
= 10 x 1 u
= 10 u

After using 14 50-cent coins, the value of 50-cent coins is 180¢ more than the value of 10-cent coins. If another 180¢ is added to the 10-cent coins, the total value of 50-cent coins and 10-cent coins will be the same.

50 u - 500 = 10 u + 180
50 u - 10 u = 180 + 500
40 u = 680

1 u = 680 ÷ 40 = 17

Number of coins that Valen had at first
= 1 u + 1 u + 4
= 2 u + 4
= (2 x 17) + 4
= 34 + 4
= 38

Answer(s): 38