Three women, Ivory, Nora and Vanessa went on a shopping spree. 90% of Ivory's spending was equal to ¹₂ of Nora's spending. Vanessa's spending was  25% less than Nora's. If Nora spent $801 less, she would spend the same amount of money as Vanessa.

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

Ivory	Nora	Vanessa
5x4	9x4
	4x9	3x9
20 u	36 u	27 u

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

910 of Ivory's spending = 12 of Nora's spending
910 of Ivory's spending =1x92x9 of Nora's spending
910 of Ivory's spending = 918 of Nora's spending

Ivory : Nora
10 : 18
5 : 9

Vanessa's spending in percent when compared to Nora's
= 100% - 25%
= 75%

Nora : Vanessa
100 : 75
4 : 3

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

Ivory : Nora : Vanessa
20 : 36 : 27

(b)

	Ivory	Nora	Vanessa
Before	20 u	36 u	27 u
Change		- 9 u
After	20 u	27 u	27 u

Additional amount that Nora would have to spend less to be the same as Vanessa
= 36 u - 27 u
= 9 u

9 u = 801

1 u = 801 ÷ 9 = 89

Amount that Vanessa spent
= 27 u
= 27 x 89
= $2403 

Answer(s): (a) 20 : 36 : 27; (b) $2403