If Natalie gives Cody $20, the amount of money she has will be 40% of his. If Cody gives Natalie $10, he will have the same amount of money as her. How much money did each of them have?
(a) Cody
(b) Natalie

	Case 1		Case 2
	Cody	Natalie	Cody	Natalie
Before	5 u - 20	2 u + 20	3.5 u + 10	3.5 u - 10
Change	+ 20	- 20	- 10	+ 10
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 20 = 3.5 u + 10
5 u - 3.5 u = 10 + 20
1.5 u = 30 

1 u = 30 ÷ 1.5 = 20

Amount that Cody has
= 5 u - 20
= 5 x 20 - 20
= 100 - 20
= $80 

(b)
Amount that Natalie has
= 2 u + 20
= 2 x 20 + 20
= 40 + 20
= $60

Answer(s): (a) $80; (b) $60