Three women, Anna, Penelope and Emily went on a shopping spree. 70% of Anna's spending was equal to ¹₅ of Penelope's spending. Emily's spending was  25% less than Penelope's. If Penelope spent $490 less, she would spend the same amount of money as Emily.

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

Anna	Penelope	Emily
2x4	7x4
	4x7	3x7
8 u	28 u	21 u

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

710 of Anna's spending = 15 of Penelope's spending
710 of Anna's spending =1x75x7 of Penelope's spending
710 of Anna's spending = 735 of Penelope's spending

Anna : Penelope
10 : 35
2 : 7

Emily's spending in percent when compared to Penelope's
= 100% - 25%
= 75%

Penelope : Emily
100 : 75
4 : 3

Penelope's spending is the repeated identity.  Make Penelope's spending the same.  LCM of 7 and 4 is 28.

Anna : Penelope : Emily
8 : 28 : 21

(b)

	Anna	Penelope	Emily
Before	8 u	28 u	21 u
Change		- 7 u
After	8 u	21 u	21 u

Additional amount that Penelope would have to spend less to be the same as Emily
= 28 u - 21 u
= 7 u

7 u = 490

1 u = 490 ÷ 7 = 70

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

Answer(s): (a) 8 : 28 : 21; (b) $1470