Three women, Cathy, Nora and Kimberly went on a shopping spree. 70% of Cathy's spending was equal to ¹₅ of Nora's spending. Kimberly's spending was  70% less than Nora's. If Nora spent $3087 less, she would spend the same amount of money as Kimberly.

1. Find the ratio of Cathy's spending to Nora's to Kimberly's.
2. How much did Kimberly spend?

Cathy	Nora	Kimberly
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

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

710 of Cathy's spending = 15 of Nora's spending
710 of Cathy's spending =1x75x7 of Nora's spending
710 of Cathy's spending = 735 of Nora's spending

Cathy : Nora
10 : 35
2 : 7

Kimberly's spending in percent when compared to Nora's
= 100% - 70%
= 30%

Nora : Kimberly
100 : 30
10 : 3

Nora's spending is the repeated identity.  Make Nora's spending the same.  LCM of 7 and 10 is 70.

Cathy : Nora : Kimberly
20 : 70 : 21

(b)

	Cathy	Nora	Kimberly
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

Additional amount that Nora would have to spend less to be the same as Kimberly
= 70 u - 21 u
= 49 u

49 u = 3087

1 u = 3087 ÷ 49 = 63

Amount that Kimberly spent
= 21 u
= 21 x 63
= $1323 

Answer(s): (a) 20 : 70 : 21; (b) $1323