The number of five-cent coins in a bottle was ¹₄ the number of twenty-cent coins. Luke took out 24 twenty-cent coins and exchanged them for five-cent coins. Then he put the money back into the bottle. The number of twenty-cent coins became ³₅ the number of five-cent coins. How much money was there in the bottle?

	Make u the same (1)x4 = (3)	5-cent (1)	20-cent (2)
Before	4 u	1 u	4 u
Change	+ 384	+ 96	- 24
After	20 p	5 p	3 p

Value of 20-cent coins to be exchanged to 5-cent coins
= 24 x 20
= 480

Number of 5-cent coins to be exchanged from the 20-cent coins
= 480 ÷ 5
= 96

(3) = (2)
20 p - 384 = 3 p + 24
20 p - 3 p = 24 + 384
17 p = 408

1 p = 408 ÷ 17 = 24

Number of 5-cent coins in the end
= 5 p
= 5 p x 24
= 120

Value of 5-cent coins in the end
= 120 x 5
= 600¢

Number of 20-cent coins in the end
= 3 p
= 3 x 24
= 72

Value of 20-cent coins in the end
= 72 x 20
= 1440¢

Total value of coins
= 600 + 1440
= 2040¢

$1 = 100¢
2040¢ = $20.40 

Answer(s): $20.40