Method 1
Value of those twenty 20¢ coins Jenny exchanged = 20¢ × 20 = 400¢ (or $4)
Number of 50¢ coins Jenny got from the neighbour in exchange = 400¢ ÷ 50¢ = 8
Since the value of each type of coin is the same after the the exchange,
2 × 50¢ = 100¢, 5 × 20¢ = 100¢
Every two 50¢ coins are equal in value to every five 20¢ coins.
Ratio of value of 20¢ to value of 50¢ now = 5 : 2
At first :
20¢ coins → 3 units, 50¢ coins →1 unit
Ratio of the number of 20¢ to 50¢ coins at first = 3 : 1 = 6 : 2
(We change to 6 : 2 to make division of the units easier. See the next working)
Following the ratio,
we let number of 50¢ coins at first be 2 units.
Number of 20¢ coins at first be 6 units.

Number of 50¢ coins now = 2 units + 8
Since the ratio of value of 20¢ to value of 50¢ now = 5 : 2,
Number of 20¢ coins now = (2 units + 8) ÷ 2 × 5
= (1 unit + 4) × 5
= 5 units + 20
Number of 20¢ coins at first = 5 units + 20 + 20
= 5 units + 40
But, we know that number of 20¢ coins at first = 6 units
So 5 units + 40 = 6 units
40 = 6 units - 5 units = 1 unit
Number of 20¢ coins at first = 6 units = 6 × 40 = 240
Value of 20¢ at first = 240 × 20¢ = 4800¢ = $48