If Dana gives Sam $18, the amount of money she has will be 30% of his. If Sam gives Dana $143, he will have the same amount of money as her. How much money did each of them have?
(a) Sam
(b) Dana

	Case 1		Case 2
	Sam	Dana	Sam	Dana
Before	10 u - 18	3 u + 18	6.5 u + 143	6.5 u - 143
Change	+ 18	- 18	- 143	+ 143
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Sam gives to Dana, there is an internal transfer of money from Sam to Dana. 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 Dana and Sam have
= 10 u + 3 u
= 13 u

Amount that Dana and Sam each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 18 = 6.5 u + 143
10 u - 6.5 u = 143 + 18
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Sam has
= 10 u - 18
= 10 x 46 - 18
= 460 - 18
= $442 

(b)
Amount that Dana has
= 3 u + 18
= 3 x 46 + 18
= 138 + 18
= $156

Answer(s): (a) $442; (b) $156