Three women, Victoria, Sarah and Cathy went on a shopping spree. 90% of Victoria's spending was equal to ¹₂ of Sarah's spending. Cathy's spending was  25% more than Sarah's. If Sarah spent another $639, she would spend the same amount of money as Cathy.

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

Victoria	Sarah	Cathy
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Victoria's spending is equal to ¹₂ of Sarah's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Victoria's spending = 12 of Sarah's spending
910 of Victoria's spending =1x92x9 of Sarah's spending
910 of Victoria's spending = 918 of Sarah's spending

Victoria : Sarah
10 : 18
5 : 9

Cathy's spending in percent when compared to Sarah's
= 100% + 25%
= 125%

Sarah : Cathy
100 : 125
4 : 5

Sarah's spending is the repeated identity.  Make Sarah's spending the same.  LCM of 9 and 4 is 36.

Victoria : Sarah : Cathy
20 : 36 : 45

(b)

	Victoria	Sarah	Cathy
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

Additional amount that Sarah would have to spend to be the same as Cathy
= 45 u - 36 u
= 9 u

9 u = 639

1 u = 639 ÷ 9 = 71

Amount that Victoria spent
= 20 u
= 20 x 71
= $1420 

Answer(s): (a) 20 : 36 : 45; (b) $1420