The number of ten-cent coins in a coin box was ¹₃ the number of fifty-cent coins. Michael took out 19 fifty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the coin box. The number of fifty-cent coins became ⁵₈ the number of ten-cent coins. How much money was there in the coin box?

	Make u the same (1)x3 = (3)	10-cent (1)	50-cent (2)
Before	3 u	1 u	3 u
Change	+ 285	+ 95	- 19
After	24 p	8 p	5 p

Value of 50-cent coins to be exchanged to 10-cent coins
= 19 x 50
= 950

Number of 10-cent coins to be exchanged from the 50-cent coins
= 950 ÷ 10
= 95

(3) = (2)
24 p - 285 = 5 p + 19
24 p - 5 p = 19 + 285
19 p = 304

1 p = 304 ÷ 19 = 16

Number of 10-cent coins in the end
= 8 p
= 8 p x 16
= 128

Value of 10-cent coins in the end
= 128 x 10
= 1280¢

Number of 50-cent coins in the end
= 5 p
= 5 x 16
= 80

Value of 50-cent coins in the end
= 80 x 50
= 4000¢

Total value of coins
= 1280 + 4000
= 5280¢

$1 = 100¢
5280¢ = $52.80 

Answer(s): $52.80