Three women, Nicole, Diana and Ivory went on a shopping spree. 70% of Nicole's spending was equal to ¹₅ of Diana's spending. Ivory's spending was  60% more than Diana's. If Diana spent another $1722, she would spend the same amount of money as Ivory.

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

Nicole	Diana	Ivory
2x5	7x5
	5x7	8x7
10 u	35 u	56 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Nicole's spending is equal to ¹₅ of Diana's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Nicole's spending = 15 of Diana's spending
710 of Nicole's spending =1x75x7 of Diana's spending
710 of Nicole's spending = 735 of Diana's spending

Nicole : Diana
10 : 35
2 : 7

Ivory's spending in percent when compared to Diana's
= 100% + 60%
= 160%

Diana : Ivory
100 : 160
5 : 8

Diana's spending is the repeated identity.  Make Diana's spending the same.  LCM of 7 and 5 is 35.

Nicole : Diana : Ivory
10 : 35 : 56

(b)

	Nicole	Diana	Ivory
Before	10 u	35 u	56 u
Change		+ 21 u
After	10 u	56 u	56 u

Additional amount that Diana would have to spend to be the same as Ivory
= 56 u - 35 u
= 21 u

21 u = 1722

1 u = 1722 ÷ 21 = 82

Amount that Nicole spent
= 10 u
= 10 x 82
= $820 

Answer(s): (a) 10 : 35 : 56; (b) $820