Three women, Barbara, Nicole and Zara went on a shopping spree. 90% of Barbara's spending was equal to ¹₅ of Nicole's spending. Zara's spending was  60% more than Nicole's. If Nicole spent another $2673, she would spend the same amount of money as Zara.

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

Barbara	Nicole	Zara
2x5	9x5
	5x9	8x9
10 u	45 u	72 u

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

910 of Barbara's spending = 15 of Nicole's spending
910 of Barbara's spending =1x95x9 of Nicole's spending
910 of Barbara's spending = 945 of Nicole's spending

Barbara : Nicole
10 : 45
2 : 9

Zara's spending in percent when compared to Nicole's
= 100% + 60%
= 160%

Nicole : Zara
100 : 160
5 : 8

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

Barbara : Nicole : Zara
10 : 45 : 72

(b)

	Barbara	Nicole	Zara
Before	10 u	45 u	72 u
Change		+ 27 u
After	10 u	72 u	72 u

Additional amount that Nicole would have to spend to be the same as Zara
= 72 u - 45 u
= 27 u

27 u = 2673

1 u = 2673 ÷ 27 = 99

Amount that Barbara spent
= 10 u
= 10 x 99
= $990 

Answer(s): (a) 10 : 45 : 72; (b) $990