Ethan has 6 more 20-cent coins than 10-cent coins. After he used 11 of his 20-cent coins, the total value of 20-cent coins is $4.90 more than the total value of 10-cent coins. How many coins did he have at first?

	20¢	10¢
Before	1 u + 6	1 u
Change	- 11
After	1 u - 5	1 u

	20¢	10¢
Number	1 u - 5	1 u
Value	20	10
Total value	20 u - 100	10 u

$1 = 100¢
$4.90 = 490¢

Number of 20¢ coins in the end
= 1 u + 6 - 11
= 1 u - 5

Total value of 20¢ coins in the end
= 20 x (1 u - 5)
= 20 u - 100

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

After using 11 20-cent coins, the value of 20-cent coins is 490¢ more than the value of 10-cent coins. If another 490¢ is added to the 10-cent coins, the total value of 20-cent coins and 10-cent coins will be the same.

20 u - 100 = 10 u + 490
20 u - 10 u = 490 + 100
10 u = 590

1 u = 590 ÷ 10 = 59

Number of coins that Ethan had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 59) + 6
= 118 + 6
= 124

Answer(s): 124