Three women, Risa, Kathy and Nicole went on a shopping spree. 90% of Risa's spending was equal to ¹₅ of Kathy's spending. Nicole's spending was  80% less than Kathy's. If Kathy spent $3204 less, she would spend the same amount of money as Nicole.

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

Risa	Kathy	Nicole
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

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

910 of Risa's spending = 15 of Kathy's spending
910 of Risa's spending =1x95x9 of Kathy's spending
910 of Risa's spending = 945 of Kathy's spending

Risa : Kathy
10 : 45
2 : 9

Nicole's spending in percent when compared to Kathy's
= 100% - 80%
= 20%

Kathy : Nicole
100 : 20
5 : 1

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

Risa : Kathy : Nicole
10 : 45 : 9

(b)

	Risa	Kathy	Nicole
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

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

36 u = 3204

1 u = 3204 ÷ 36 = 89

Amount that Nicole spent
= 9 u
= 9 x 89
= $801 

Answer(s): (a) 10 : 45 : 9; (b) $801