If Mary gives Glen $26, the amount of money she has will be 40% of his. If Glen gives Mary $31, he will have the same amount of money as her. How much money did each of them have?
(a) Glen
(b) Mary

	Case 1		Case 2
	Glen	Mary	Glen	Mary
Before	5 u - 26	2 u + 26	3.5 u + 31	3.5 u - 31
Change	+ 26	- 26	- 31	+ 31
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Glen gives to Mary, there is an internal transfer of money from Glen to Mary. 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 Mary and Glen have
= 5 u + 2 u
= 7 u

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

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

5 u - 26 = 3.5 u + 31
5 u - 3.5 u = 31 + 26
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Glen has
= 5 u - 26
= 5 x 38 - 26
= 190 - 26
= $164 

(b)
Amount that Mary has
= 2 u + 26
= 2 x 38 + 26
= 76 + 26
= $102

Answer(s): (a) $164; (b) $102