The number of ten-cent coins in a jar was 1/3 the number of fifty-cent coins. Zane took out 19 fifty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the jar. The number of fifty-cent coins became 5/8 the number of ten-cent coins. How much money was there in the jar?

Answer 1

Starting with t 10¢ coins and f 50¢ coins,
t = 1/3 f
after the switch,
f-19 = 5/8 (t + 19)
solving those two equations,
f-19 = 5/8 (f/3+19)
f = 39

Answer 2

Ten 20-cent coins exchanged for four 80-cent coins
A first, ratio = 3:2
20 cent = 34
50 cent = 24
Exchanged
20 cent = -10
50 cent = +4
In the end
20 cent = 34 - 10
50 cent = 24 + 4
Given ratio in the end is 7:10
7:10 = (34 - 10) : (24 + 4)
6 = 8
Sum of money = 4.8 + 8
= $12.80