Three women, Pamela, Raeann and Shiyun went on a shopping spree. 70% of Pamela's spending was equal to ¹₆ of Raeann's spending. Shiyun's spending was  60% more than Raeann's. If Raeann spent another $5544, she would spend the same amount of money as Shiyun.

1. Find the ratio of Pamela's spending to Raeann's to Shiyun's.
2. How much did Pamela spend?

Pamela	Raeann	Shiyun
5x5	21x5
	5x21	8x21
25 u	105 u	168 u

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

710 of Pamela's spending = 16 of Raeann's spending
710 of Pamela's spending =1x76x7 of Raeann's spending
710 of Pamela's spending = 742 of Raeann's spending

Pamela : Raeann
10 : 42
5 : 21

Shiyun's spending in percent when compared to Raeann's
= 100% + 60%
= 160%

Raeann : Shiyun
100 : 160
5 : 8

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

Pamela : Raeann : Shiyun
25 : 105 : 168

(b)

	Pamela	Raeann	Shiyun
Before	25 u	105 u	168 u
Change		+ 63 u
After	25 u	168 u	168 u

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

63 u = 5544

1 u = 5544 ÷ 63 = 88

Amount that Pamela spent
= 25 u
= 25 x 88
= $2200 

Answer(s): (a) 25 : 105 : 168; (b) $2200