Three women, Victoria, Tammy and Olivia went on a shopping spree. 30% of Victoria's spending was equal to ¹₆ of Tammy's spending. Olivia's spending was  25% more than Tammy's. If Tammy spent another $261, she would spend the same amount of money as Olivia.

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

Victoria	Tammy	Olivia
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Victoria's spending is equal to ¹₆ of Tammy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Victoria's spending = 16 of Tammy's spending
310 of Victoria's spending =1x36x3 of Tammy's spending
310 of Victoria's spending = 318 of Tammy's spending

Victoria : Tammy
10 : 18
5 : 9

Olivia's spending in percent when compared to Tammy's
= 100% + 25%
= 125%

Tammy : Olivia
100 : 125
4 : 5

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

Victoria : Tammy : Olivia
20 : 36 : 45

(b)

	Victoria	Tammy	Olivia
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 261

1 u = 261 ÷ 9 = 29

Amount that Victoria spent
= 20 u
= 20 x 29
= $580 

Answer(s): (a) 20 : 36 : 45; (b) $580