Three women, Rachel, Fanny and Nora went on a shopping spree. 30% of Rachel's spending was equal to ¹₅ of Fanny's spending. Nora's spending was  40% more than Fanny's. If Fanny spent another $480, she would spend the same amount of money as Nora.

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

Rachel	Fanny	Nora
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Rachel's spending is equal to ¹₅ of Fanny's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Rachel's spending = 15 of Fanny's spending
310 of Rachel's spending =1x35x3 of Fanny's spending
310 of Rachel's spending = 315 of Fanny's spending

Rachel : Fanny
10 : 15
2 : 3

Nora's spending in percent when compared to Fanny's
= 100% + 40%
= 140%

Fanny : Nora
100 : 140
5 : 7

Fanny's spending is the repeated identity.  Make Fanny's spending the same.  LCM of 3 and 5 is 15.

Rachel : Fanny : Nora
10 : 15 : 21

(b)

	Rachel	Fanny	Nora
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Fanny would have to spend to be the same as Nora
= 21 u - 15 u
= 6 u

6 u = 480

1 u = 480 ÷ 6 = 80

Amount that Rachel spent
= 10 u
= 10 x 80
= $800 

Answer(s): (a) 10 : 15 : 21; (b) $800