If Natalie gives Luke $19, the amount of money she has will be 75% of his. If Luke gives Natalie $2, he will have the same amount of money as her. How much money did each of them have?
(a) Luke
(b) Natalie

	Case 1		Case 2
	Luke	Natalie	Luke	Natalie
Before	4 u - 19	3 u + 19	3.5 u + 2	3.5 u - 2
Change	+ 19	- 19	- 2	+ 2
After	4 u	3 u	3.5 u	3.5 u

(a)
75% = ⁷⁵₁₀₀ = ³₄

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

In Case 2, when Luke gives to Natalie, there is an internal transfer of money from Luke 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 Luke have
= 4 u + 3 u
= 7 u

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

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

4 u - 19 = 3.5 u + 2
4 u - 3.5 u = 2 + 19
0.5 u = 21 

1 u = 21 ÷ 0.5 = 42

Amount that Luke has
= 4 u - 19
= 4 x 42 - 19
= 168 - 19
= $149 

(b)
Amount that Natalie has
= 3 u + 19
= 3 x 42 + 19
= 126 + 19
= $145

Answer(s): (a) $149; (b) $145