Three women, Nicole, Kathy and Vanessa went on a shopping spree. 30% of Nicole's spending was equal to ¹₆ of Kathy's spending. Vanessa's spending was  50% more than Kathy's. If Kathy spent another $873, she would spend the same amount of money as Vanessa.

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

Nicole	Kathy	Vanessa
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Nicole's spending is equal to ¹₆ of Kathy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Nicole's spending = 16 of Kathy's spending
310 of Nicole's spending =1x36x3 of Kathy's spending
310 of Nicole's spending = 318 of Kathy's spending

Nicole : Kathy
10 : 18
5 : 9

Vanessa's spending in percent when compared to Kathy's
= 100% + 50%
= 150%

Kathy : Vanessa
100 : 150
2 : 3

Kathy's spending is the repeated identity.  Make Kathy's spending the same.  LCM of 9 and 2 is 18.

Nicole : Kathy : Vanessa
10 : 18 : 27

(b)

	Nicole	Kathy	Vanessa
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Kathy would have to spend to be the same as Vanessa
= 27 u - 18 u
= 9 u

9 u = 873

1 u = 873 ÷ 9 = 97

Amount that Nicole spent
= 10 u
= 10 x 97
= $970 

Answer(s): (a) 10 : 18 : 27; (b) $970