If Ivory gives Vaidev $36, the amount of money she has will be 30% of his. If Vaidev gives Ivory $97, he will have the same amount of money as her. How much money did each of them have?
(a) Vaidev
(b) Ivory

	Case 1		Case 2
	Vaidev	Ivory	Vaidev	Ivory
Before	10 u - 36	3 u + 36	6.5 u + 97	6.5 u - 97
Change	+ 36	- 36	- 97	+ 97
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Vaidev gives to Ivory, there is an internal transfer of money from Vaidev 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 Vaidev have
= 10 u + 3 u
= 13 u

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

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

10 u - 36 = 6.5 u + 97
10 u - 6.5 u = 97 + 36
3.5 u = 133 

1 u = 133 ÷ 3.5 = 38

Amount that Vaidev has
= 10 u - 36
= 10 x 38 - 36
= 380 - 36
= $344 

(b)
Amount that Ivory has
= 3 u + 36
= 3 x 38 + 36
= 114 + 36
= $150

Answer(s): (a) $344; (b) $150