Ivan has 5 more 50-cent coins than 10-cent coins. After he used 15 of his 50-cent coins, the total value of 50-cent coins is $3.40 more than the total value of 10-cent coins. How many coins did he have at first?

	50¢	10¢
Before	1 u + 5	1 u
Change	- 15
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¢
$3.40 = 340¢

Number of 50¢ coins in the end
= 1 u + 5 - 15
= 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 15 50-cent coins, the value of 50-cent coins is 340¢ more than the value of 10-cent coins. If another 340¢ 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 + 340
50 u - 10 u = 340 + 500
40 u = 840

1 u = 840 ÷ 40 = 21

Number of coins that Ivan had at first
= 1 u + 1 u + 5
= 2 u + 5
= (2 x 21) + 5
= 42 + 5
= 47

Answer(s): 47