Three women, Risa, Emily and Fanny went on a shopping spree. 30% of Risa's spending was equal to ¹₆ of Emily's spending. Fanny's spending was  40% more than Emily's. If Emily spent another $1998, she would spend the same amount of money as Fanny.

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

Risa	Emily	Fanny
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

310 of Risa's spending = 16 of Emily's spending
310 of Risa's spending =1x36x3 of Emily's spending
310 of Risa's spending = 318 of Emily's spending

Risa : Emily
10 : 18
5 : 9

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

Emily : Fanny
100 : 140
5 : 7

Emily's spending is the repeated identity.  Make Emily's spending the same.  LCM of 9 and 5 is 45.

Risa : Emily : Fanny
25 : 45 : 63

(b)

	Risa	Emily	Fanny
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Emily would have to spend to be the same as Fanny
= 63 u - 45 u
= 18 u

18 u = 1998

1 u = 1998 ÷ 18 = 111

Amount that Risa spent
= 25 u
= 25 x 111
= $2775 

Answer(s): (a) 25 : 45 : 63; (b) $2775