If Ivory gives John $40, the amount of money she has will be 40% of his. If John gives Ivory $8, he will have the same amount of money as her. How much money did each of them have?
(a) John
(b) Ivory

	Case 1		Case 2
	John	Ivory	John	Ivory
Before	5 u - 40	2 u + 40	3.5 u + 8	3.5 u - 8
Change	+ 40	- 40	- 8	+ 8
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 40 = 3.5 u + 8
5 u - 3.5 u = 8 + 40
1.5 u = 48 

1 u = 48 ÷ 1.5 = 32

Amount that John has
= 5 u - 40
= 5 x 32 - 40
= 160 - 40
= $120 

(b)
Amount that Ivory has
= 2 u + 40
= 2 x 32 + 40
= 64 + 40
= $104

Answer(s): (a) $120; (b) $104