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

	Case 1		Case 2
	Fred	Sarah	Fred	Sarah
Before	5 u - 40	2 u + 40	3.5 u + 35	3.5 u - 35
Change	+ 40	- 40	- 35	+ 35
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 40 = 3.5 u + 35
5 u - 3.5 u = 35 + 40
1.5 u = 75 

1 u = 75 ÷ 1.5 = 50

Amount that Fred has
= 5 u - 40
= 5 x 50 - 40
= 250 - 40
= $210 

(b)
Amount that Sarah has
= 2 u + 40
= 2 x 50 + 40
= 100 + 40
= $140

Answer(s): (a) $210; (b) $140