Jolens and Penny had a sum of money. Jolene gave Penny 0.4 of her money. Penny then gave Jolene 1/2 of her money. In the end, Jolene had three times the amount of money that penny had. If Jolene gave penny $125 more than what Penny Gave Jolene, How much money did Jolene have at first ?

For this question they each give to each other, so the totals remain the same throughout. We can just work backwards using ratios to solve it.

J : P

3 : 1 (At end & After Jolene gave 50% to Penny)

2 : 2 (Before Penny gave 50% to Jolene)

3 : 3 (Change to a ratio that has 6/10 left --> 3/5)

5 : 1 (At first, before Jolene gave 40% to Penny)

The question asks us to compare the number of units they gave to each other. So we need to ensure the ratios are comparable throughout. If you notice I originally changed the ratio of 2 : 2 to 3 : 3 in the middle so that we could take 50%.

J : P

9 : 3 (At end & After Jolene gave 50% to Penny)

6 : 6 (After Jolene gave 40% and before Penny gave 50%)

10 : 2 (At first, before Jolene gave 40% to Penny)

Jolene gave to Penny 4units

Penny gave to Jolene 3units

difference is 1unit

1unit --> $125

Jolene at first $1250