The number of ten-cent coins in a bottle was ¹₃ the number of twenty-cent coins. Archie took out 24 twenty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the bottle. The number of twenty-cent coins became ³₈ the number of ten-cent coins. How much money was there in the bottle?

	Make u the same (1)x3 = (3)	10-cent (1)	20-cent (2)
Before	3 u	1 u	3 u
Change	+ 144	+ 48	- 24
After	24 p	8 p	3 p

Value of 20-cent coins to be exchanged to 10-cent coins
= 24 x 20
= 480

Number of 10-cent coins to be exchanged from the 20-cent coins
= 480 ÷ 10
= 48

(3) = (2)
24 p - 144 = 3 p + 24
24 p - 3 p = 24 + 144
21 p = 168

1 p = 168 ÷ 21 = 8

Number of 10-cent coins in the end
= 8 p
= 8 p x 8
= 64

Value of 10-cent coins in the end
= 64 x 10
= 640¢

Number of 20-cent coins in the end
= 3 p
= 3 x 8
= 24

Value of 20-cent coins in the end
= 24 x 20
= 480¢

Total value of coins
= 640 + 480
= 1120¢

$1 = 100¢
1120¢ = $11.20 

Answer(s): $11.20