Three women, Victoria, Yen and Nicole went on a shopping spree. 30% of Victoria's spending was equal to ¹₂ of Yen's spending. Nicole's spending was  40% more than Yen's. If Yen spent another $132, she would spend the same amount of money as Nicole.

1. Find the ratio of Victoria's spending to Yen's to Nicole's.
2. How much did Victoria spend?

Victoria	Yen	Nicole
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Victoria's spending is equal to ¹₂ of Yen's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Victoria's spending = 12 of Yen's spending
310 of Victoria's spending =1x32x3 of Yen's spending
310 of Victoria's spending = 36 of Yen's spending

Victoria : Yen
10 : 6
5 : 3

Nicole's spending in percent when compared to Yen's
= 100% + 40%
= 140%

Yen : Nicole
100 : 140
5 : 7

Yen's spending is the repeated identity.  Make Yen's spending the same.  LCM of 3 and 5 is 15.

Victoria : Yen : Nicole
25 : 15 : 21

(b)

	Victoria	Yen	Nicole
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

Additional amount that Yen would have to spend to be the same as Nicole
= 21 u - 15 u
= 6 u

6 u = 132

1 u = 132 ÷ 6 = 22

Amount that Victoria spent
= 25 u
= 25 x 22
= $550 

Answer(s): (a) 25 : 15 : 21; (b) $550