If Min gives Rael $35, the amount of money she has will be 40% of his. If Rael gives Min $31, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Min

	Case 1		Case 2
	Rael	Min	Rael	Min
Before	5 u - 35	2 u + 35	3.5 u + 31	3.5 u - 31
Change	+ 35	- 35	- 31	+ 31
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 35 = 3.5 u + 31
5 u - 3.5 u = 31 + 35
1.5 u = 66 

1 u = 66 ÷ 1.5 = 44

Amount that Rael has
= 5 u - 35
= 5 x 44 - 35
= 220 - 35
= $185 

(b)
Amount that Min has
= 2 u + 35
= 2 x 44 + 35
= 88 + 35
= $123

Answer(s): (a) $185; (b) $123