Three women, Anna, Penelope and Roshel went on a shopping spree. 70% of Anna's spending was equal to ¹₆ of Penelope's spending. Roshel's spending was  25% more than Penelope's. If Penelope spent another $1722, she would spend the same amount of money as Roshel.

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

Anna	Penelope	Roshel
5x4	21x4
	4x21	5x21
20 u	84 u	105 u

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

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

Anna : Penelope
10 : 42
5 : 21

Roshel's spending in percent when compared to Penelope's
= 100% + 25%
= 125%

Penelope : Roshel
100 : 125
4 : 5

Penelope's spending is the repeated identity.  Make Penelope's spending the same.  LCM of 21 and 4 is 84.

Anna : Penelope : Roshel
20 : 84 : 105

(b)

	Anna	Penelope	Roshel
Before	20 u	84 u	105 u
Change		+ 21 u
After	20 u	105 u	105 u

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

21 u = 1722

1 u = 1722 ÷ 21 = 82

Amount that Anna spent
= 20 u
= 20 x 82
= $1640 

Answer(s): (a) 20 : 84 : 105; (b) $1640