²₃ of Liam's savings comprised of 10-cent coins and 50-cent coins. Liam used some 10-cent coins to purchase a lego set. The number of 50-cent coins left was 40% more than the number of 10-cent coins left. Given that Liam had 20 more 50-cent coins than 10-cent coins left in the end, find the amount of money Liam spent on the lego set.

	10-cent coins	50-cent coins
Before	2x7 = 14 u	1x7 = 7 u
Change	- 9 u
After	5x1 = 5 u	7x1 = 7 u

Fraction of Liam's savings that comprised of 50-cent coins
= 1 - ²₃
= ¹₃

Number of 50-cents coins in the end in percentage
= 100% + 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Number of 50-cent coins remains unchanged. Make the number of 50-cent coins the same.  LCM of 1 and 7 is 7.

Number of more 50-cent coins than 10-cent coins
= 7 u - 5 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of 10-cent coins spent on the lego set 
= 14 u - 5 u
= 9 u
= 9 x 10
= 90

Amount that Liam spent on the lego set 
= 90 x 0.1
= $9

Answer(s): $9