Three women, Rachel, Lynn and Dana went on a shopping spree. 70% of Rachel's spending was equal to ¹₆ of Lynn's spending. Dana's spending was  60% more than Lynn's. If Lynn spent another $1953, she would spend the same amount of money as Dana.

1. Find the ratio of Rachel's spending to Lynn's to Dana's.
2. How much did Rachel spend?

Rachel	Lynn	Dana
5x5	21x5
	5x21	8x21
25 u	105 u	168 u

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

710 of Rachel's spending = 16 of Lynn's spending
710 of Rachel's spending =1x76x7 of Lynn's spending
710 of Rachel's spending = 742 of Lynn's spending

Rachel : Lynn
10 : 42
5 : 21

Dana's spending in percent when compared to Lynn's
= 100% + 60%
= 160%

Lynn : Dana
100 : 160
5 : 8

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

Rachel : Lynn : Dana
25 : 105 : 168

(b)

	Rachel	Lynn	Dana
Before	25 u	105 u	168 u
Change		+ 63 u
After	25 u	168 u	168 u

Additional amount that Lynn would have to spend to be the same as Dana
= 168 u - 105 u
= 63 u

63 u = 1953

1 u = 1953 ÷ 63 = 31

Amount that Rachel spent
= 25 u
= 25 x 31
= $775 

Answer(s): (a) 25 : 105 : 168; (b) $775