Three women, Cindy, Penelope and Nora went on a shopping spree. 70% of Cindy's spending was equal to ¹₆ of Penelope's spending. Nora's spending was  80% less than Penelope's. If Penelope spent $3108 less, she would spend the same amount of money as Nora.

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

Cindy	Penelope	Nora
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

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

710 of Cindy's spending = 16 of Penelope's spending
710 of Cindy's spending =1x76x7 of Penelope's spending
710 of Cindy's spending = 742 of Penelope's spending

Cindy : Penelope
10 : 42
5 : 21

Nora's spending in percent when compared to Penelope's
= 100% - 80%
= 20%

Penelope : Nora
100 : 20
5 : 1

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

Cindy : Penelope : Nora
25 : 105 : 21

(b)

	Cindy	Penelope	Nora
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

Additional amount that Penelope would have to spend less to be the same as Nora
= 105 u - 21 u
= 84 u

84 u = 3108

1 u = 3108 ÷ 84 = 37

Amount that Nora spent
= 21 u
= 21 x 37
= $777 

Answer(s): (a) 25 : 105 : 21; (b) $777