Three women, Shannon, Vanessa and Emma went on a shopping spree. 90% of Shannon's spending was equal to ¹₂ of Vanessa's spending. Emma's spending was  25% more than Vanessa's. If Vanessa spent another $324, she would spend the same amount of money as Emma.

1. Find the ratio of Shannon's spending to Vanessa's to Emma's.
2. How much did Shannon spend?

Shannon	Vanessa	Emma
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

910 of Shannon's spending = 12 of Vanessa's spending
910 of Shannon's spending =1x92x9 of Vanessa's spending
910 of Shannon's spending = 918 of Vanessa's spending

Shannon : Vanessa
10 : 18
5 : 9

Emma's spending in percent when compared to Vanessa's
= 100% + 25%
= 125%

Vanessa : Emma
100 : 125
4 : 5

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

Shannon : Vanessa : Emma
20 : 36 : 45

(b)

	Shannon	Vanessa	Emma
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 324

1 u = 324 ÷ 9 = 36

Amount that Shannon spent
= 20 u
= 20 x 36
= $720 

Answer(s): (a) 20 : 36 : 45; (b) $720