If Esther gives Vaidev $20, the amount of money she has will be 75% of his. If Vaidev gives Esther $2, he will have the same amount of money as her. How much money did each of them have?
(a) Vaidev
(b) Esther

	Case 1		Case 2
	Vaidev	Esther	Vaidev	Esther
Before	4 u - 20	3 u + 20	3.5 u + 2	3.5 u - 2
Change	+ 20	- 20	- 2	+ 2
After	4 u	3 u	3.5 u	3.5 u

(a)
75% = ⁷⁵₁₀₀ = ³₄

In Case 1, when Esther gives to Vaidev, there is an internal transfer of money from Esther to Vaidev.  The total amount that both have remains the same.

In Case 2, when Vaidev gives to Esther, there is an internal transfer of money from Vaidev to Esther. The total amount that both have remains the same.

The total amount that both have in Case 1 and Case 2 are the same.

Total amount that Esther and Vaidev have
= 4 u + 3 u
= 7 u

Amount that Esther and Vaidev each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

Amount that Vaidev has at first is the same in Case 1 and Case 2.

4 u - 20 = 3.5 u + 2
4 u - 3.5 u = 2 + 20
0.5 u = 22 

1 u = 22 ÷ 0.5 = 44

Amount that Vaidev has
= 4 u - 20
= 4 x 44 - 20
= 176 - 20
= $156 

(b)
Amount that Esther has
= 3 u + 20
= 3 x 44 + 20
= 132 + 20
= $152

Answer(s): (a) $156; (b) $152