Howard has 2 more 50-cent coins than 20-cent coins. After he used 15 of his 50-cent coins, the total value of 50-cent coins is $4.60 more than the total value of 20-cent coins. How many coins did he have at first?

	50¢	20¢
Before	1 u + 2	1 u
Change	- 15
After	1 u - 13	1 u

	50¢	20¢
Number	1 u - 13	1 u
Value	50	20
Total value	50 u - 650	20 u

$1 = 100¢
$4.60 = 460¢

Number of 50¢ coins in the end
= 1 u + 2 - 15
= 1 u - 13

Total value of 50¢ coins in the end
= 50 x (1 u - 13)
= 50 u - 650

Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u

After using 15 50-cent coins, the value of 50-cent coins is 460¢ more than the value of 20-cent coins. If another 460¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.

50 u - 650 = 20 u + 460
50 u - 20 u = 460 + 650
30 u = 1110

1 u = 1110 ÷ 30 = 37

Number of coins that Howard had at first
= 1 u + 1 u + 2
= 2 u + 2
= (2 x 37) + 2
= 74 + 2
= 76

Answer(s): 76