Three women, Marion, Penelope and Kimberly went on a shopping spree. 70% of Marion's spending was equal to ¹₂ of Penelope's spending. Kimberly's spending was  70% less than Penelope's. If Penelope spent $3430 less, she would spend the same amount of money as Kimberly.

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

Marion	Penelope	Kimberly
5x10	7x10
	10x7	3x7
50 u	70 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Marion's spending is equal to ¹₂ of Penelope's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Marion's spending = 12 of Penelope's spending
710 of Marion's spending =1x72x7 of Penelope's spending
710 of Marion's spending = 714 of Penelope's spending

Marion : Penelope
10 : 14
5 : 7

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

Penelope : Kimberly
100 : 30
10 : 3

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

Marion : Penelope : Kimberly
50 : 70 : 21

(b)

	Marion	Penelope	Kimberly
Before	50 u	70 u	21 u
Change		- 49 u
After	50 u	21 u	21 u

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

49 u = 3430

1 u = 3430 ÷ 49 = 70

Amount that Kimberly spent
= 21 u
= 21 x 70
= $1470 

Answer(s): (a) 50 : 70 : 21; (b) $1470