If Yen gives Caden $27, the amount of money she has will be 40% of his. If Caden gives Yen $30, he will have the same amount of money as her. How much money did each of them have?
(a) Caden
(b) Yen

	Case 1		Case 2
	Caden	Yen	Caden	Yen
Before	5 u - 27	2 u + 27	3.5 u + 30	3.5 u - 30
Change	+ 27	- 27	- 30	+ 30
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 27 = 3.5 u + 30
5 u - 3.5 u = 30 + 27
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Caden has
= 5 u - 27
= 5 x 38 - 27
= 190 - 27
= $163 

(b)
Amount that Yen has
= 2 u + 27
= 2 x 38 + 27
= 76 + 27
= $103

Answer(s): (a) $163; (b) $103