Three women, Nicole, Victoria and Xandra went on a shopping spree. 70% of Nicole's spending was equal to ¹₂ of Victoria's spending. Xandra's spending was  25% less than Victoria's. If Victoria spent $140 less, she would spend the same amount of money as Xandra.

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

Nicole	Victoria	Xandra
5x4	7x4
	4x7	3x7
20 u	28 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Nicole's spending is equal to ¹₂ of Victoria's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Nicole's spending = 12 of Victoria's spending
710 of Nicole's spending =1x72x7 of Victoria's spending
710 of Nicole's spending = 714 of Victoria's spending

Nicole : Victoria
10 : 14
5 : 7

Xandra's spending in percent when compared to Victoria's
= 100% - 25%
= 75%

Victoria : Xandra
100 : 75
4 : 3

Victoria's spending is the repeated identity.  Make Victoria's spending the same.  LCM of 7 and 4 is 28.

Nicole : Victoria : Xandra
20 : 28 : 21

(b)

	Nicole	Victoria	Xandra
Before	20 u	28 u	21 u
Change		- 7 u
After	20 u	21 u	21 u

Additional amount that Victoria would have to spend less to be the same as Xandra
= 28 u - 21 u
= 7 u

7 u = 140

1 u = 140 ÷ 7 = 20

Amount that Xandra spent
= 21 u
= 21 x 20
= $420 

Answer(s): (a) 20 : 28 : 21; (b) $420