⁵₆ of Archie's savings comprised of 10-cent coins and 20-cent coins. Archie used some 10-cent coins to purchase a marble. The number of 20-cent coins left was 40% more than the number of 10-cent coins left. Given that Archie had 6 more 20-cent coins than 10-cent coins left in the end, find the amount of money Archie spent on the marble.

	10-cent coins	20-cent coins
Before	5x7 = 35 u	1x7 = 7 u
Change	- 30 u
After	5x1 = 5 u	7x1 = 7 u

Fraction of Archie's savings that comprised of 20-cent coins
= 1 - ⁵₆
= ¹₆

Number of 20-cents coins in the end in percentage
= 100% + 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Number of 20-cent coins remains unchanged. Make the number of 20-cent coins the same.  LCM of 1 and 7 is 7.

Number of more 20-cent coins than 10-cent coins
= 7 u - 5 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

Number of 10-cent coins spent on the marble 
= 35 u - 5 u
= 30 u
= 30 x 3
= 90

Amount that Archie spent on the marble 
= 90 x 0.1
= $9

Answer(s): $9