Three women, Kylie, Tiffany and Fanny went on a shopping spree. 90% of Kylie's spending was equal to ¹₅ of Tiffany's spending. Fanny's spending was  80% less than Tiffany's. If Tiffany spent $1692 less, she would spend the same amount of money as Fanny.

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

Kylie	Tiffany	Fanny
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Kylie's spending is equal to ¹₅ of Tiffany's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Kylie's spending = 15 of Tiffany's spending
910 of Kylie's spending =1x95x9 of Tiffany's spending
910 of Kylie's spending = 945 of Tiffany's spending

Kylie : Tiffany
10 : 45
2 : 9

Fanny's spending in percent when compared to Tiffany's
= 100% - 80%
= 20%

Tiffany : Fanny
100 : 20
5 : 1

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

Kylie : Tiffany : Fanny
10 : 45 : 9

(b)

	Kylie	Tiffany	Fanny
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

Additional amount that Tiffany would have to spend less to be the same as Fanny
= 45 u - 9 u
= 36 u

36 u = 1692

1 u = 1692 ÷ 36 = 47

Amount that Fanny spent
= 9 u
= 9 x 47
= $423 

Answer(s): (a) 10 : 45 : 9; (b) $423