Method 2 (total unchanged)
Ratio of the number of 20¢ to 50¢ coins at first = 3 : 1
Value of every three 20¢ coins = 3 × 20¢ = 60¢
Value of every 50¢ coins = 50¢ × 1 = 50¢
At first,
Ratio of the value of the 20¢ coins to the 50¢ coins to their total value
= 60 : 50 : 110 = 6 : 5 : 11 = 12 : 10 : 22
Note that the total value is unchanged.
After the exchange, there is an equal value of 20¢ and 50 ¢ coins.
Now,
Ratio of the value of 20¢ to 50¢ coins to total
= 1 : 1 : 2 = 11 : 11 : 22
(Since the total value is unchanged, We make the total value to the same number for both ratios, 22)
Value of those twenty 20¢ coins Jenny exchanged = 20¢ × 20 = 400¢ (or $4)
So Jenny exchanged $4 worth of 20¢ coins for $4 for 50¢ coins.
Comparing the two ratios, we see that the value of 20¢ coins has decreased by 1 unit. The value of 50¢ coins has increased by 1 unit.
So 1 unit = $4
Value of 20¢ at first = 12 units
= 12 × $4 = $48