If Esther gives Michael $20, the amount of money she has will be 30% of his. If Michael gives Esther $113, he will have the same amount of money as her. How much money did each of them have?
(a) Michael
(b) Esther

	Case 1		Case 2
	Michael	Esther	Michael	Esther
Before	10 u - 20	3 u + 20	6.5 u + 113	6.5 u - 113
Change	+ 20	- 20	- 113	+ 113
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Michael gives to Esther, there is an internal transfer of money from Michael 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 Michael have
= 10 u + 3 u
= 13 u

Amount that Esther and Michael each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 20 = 6.5 u + 113
10 u - 6.5 u = 113 + 20
3.5 u = 133 

1 u = 133 ÷ 3.5 = 38

Amount that Michael has
= 10 u - 20
= 10 x 38 - 20
= 380 - 20
= $360 

(b)
Amount that Esther has
= 3 u + 20
= 3 x 38 + 20
= 114 + 20
= $134

Answer(s): (a) $360; (b) $134