Three women, Fanny, Abi and Cindy went on a shopping spree. 30% of Fanny's spending was equal to ¹₂ of Abi's spending. Cindy's spending was  40% more than Abi's. If Abi spent another $438, she would spend the same amount of money as Cindy.

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

Fanny	Abi	Cindy
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Fanny's spending is equal to ¹₂ of Abi's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Fanny's spending = 12 of Abi's spending
310 of Fanny's spending =1x32x3 of Abi's spending
310 of Fanny's spending = 36 of Abi's spending

Fanny : Abi
10 : 6
5 : 3

Cindy's spending in percent when compared to Abi's
= 100% + 40%
= 140%

Abi : Cindy
100 : 140
5 : 7

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

Fanny : Abi : Cindy
25 : 15 : 21

(b)

	Fanny	Abi	Cindy
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

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

6 u = 438

1 u = 438 ÷ 6 = 73

Amount that Fanny spent
= 25 u
= 25 x 73
= $1825 

Answer(s): (a) 25 : 15 : 21; (b) $1825