Three women, Anna, Marion and Kimberly went on a shopping spree. 70% of Anna's spending was equal to ¹₆ of Marion's spending. Kimberly's spending was  60% less than Marion's. If Marion spent $7056 less, she would spend the same amount of money as Kimberly.

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

Anna	Marion	Kimberly
5x5	21x5
	5x21	2x21
25 u	105 u	42 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Anna's spending is equal to ¹₆ of Marion's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Anna's spending = 16 of Marion's spending
710 of Anna's spending =1x76x7 of Marion's spending
710 of Anna's spending = 742 of Marion's spending

Anna : Marion
10 : 42
5 : 21

Kimberly's spending in percent when compared to Marion's
= 100% - 60%
= 40%

Marion : Kimberly
100 : 40
5 : 2

Marion's spending is the repeated identity.  Make Marion's spending the same.  LCM of 21 and 5 is 105.

Anna : Marion : Kimberly
25 : 105 : 42

(b)

	Anna	Marion	Kimberly
Before	25 u	105 u	42 u
Change		- 63 u
After	25 u	42 u	42 u

Additional amount that Marion would have to spend less to be the same as Kimberly
= 105 u - 42 u
= 63 u

63 u = 7056

1 u = 7056 ÷ 63 = 112

Amount that Kimberly spent
= 42 u
= 42 x 112
= $4704 

Answer(s): (a) 25 : 105 : 42; (b) $4704