Three women, Nicole, Irene and Risa went on a shopping spree. 90% of Nicole's spending was equal to ¹₆ of Irene's spending. Risa's spending was  40% more than Irene's. If Irene spent another $5994, she would spend the same amount of money as Risa.

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

Nicole	Irene	Risa
5x5	27x5
	5x27	7x27
25 u	135 u	189 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Nicole's spending is equal to ¹₆ of Irene's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Nicole's spending = 16 of Irene's spending
910 of Nicole's spending =1x96x9 of Irene's spending
910 of Nicole's spending = 954 of Irene's spending

Nicole : Irene
10 : 54
5 : 27

Risa's spending in percent when compared to Irene's
= 100% + 40%
= 140%

Irene : Risa
100 : 140
5 : 7

Irene's spending is the repeated identity.  Make Irene's spending the same.  LCM of 27 and 5 is 135.

Nicole : Irene : Risa
25 : 135 : 189

(b)

	Nicole	Irene	Risa
Before	25 u	135 u	189 u
Change		+ 54 u
After	25 u	189 u	189 u

Additional amount that Irene would have to spend to be the same as Risa
= 189 u - 135 u
= 54 u

54 u = 5994

1 u = 5994 ÷ 54 = 111

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

Answer(s): (a) 25 : 135 : 189; (b) $2775