Three women, Emily, Diana and Penelope went on a shopping spree. 70% of Emily's spending was equal to ¹₆ of Diana's spending. Penelope's spending was  80% less than Diana's. If Diana spent $9492 less, she would spend the same amount of money as Penelope.

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

Emily	Diana	Penelope
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

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

710 of Emily's spending = 16 of Diana's spending
710 of Emily's spending =1x76x7 of Diana's spending
710 of Emily's spending = 742 of Diana's spending

Emily : Diana
10 : 42
5 : 21

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

Diana : Penelope
100 : 20
5 : 1

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

Emily : Diana : Penelope
25 : 105 : 21

(b)

	Emily	Diana	Penelope
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

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

84 u = 9492

1 u = 9492 ÷ 84 = 113

Amount that Penelope spent
= 21 u
= 21 x 113
= $2373 

Answer(s): (a) 25 : 105 : 21; (b) $2373