The number of five-cent coins in a bag was ¹₃ the number of twenty-cent coins. Harry took out 21 twenty-cent coins and exchanged them for five-cent coins. Then he put the money back into the bag. The number of twenty-cent coins became ²₅ the number of five-cent coins. How much money was there in the bag?

	Make u the same (1)x3 = (3)	5-cent (1)	20-cent (2)
Before	3 u	1 u	3 u
Change	+ 252	+ 84	- 21
After	15 p	5 p	2 p

Value of 20-cent coins to be exchanged to 5-cent coins
= 21 x 20
= 420

Number of 5-cent coins to be exchanged from the 20-cent coins
= 420 ÷ 5
= 84

(3) = (2)
15 p - 252 = 2 p + 21
15 p - 2 p = 21 + 252
13 p = 273

1 p = 273 ÷ 13 = 21

Number of 5-cent coins in the end
= 5 p
= 5 p x 21
= 105

Value of 5-cent coins in the end
= 105 x 5
= 525¢

Number of 20-cent coins in the end
= 2 p
= 2 x 21
= 42

Value of 20-cent coins in the end
= 42 x 20
= 840¢

Total value of coins
= 525 + 840
= 1365¢

$1 = 100¢
1365¢ = $13.65 

Answer(s): $13.65