Three women, Shiyun, Raeann and Anna went on a shopping spree. 70% of Shiyun's spending was equal to ¹₆ of Raeann's spending. Anna's spending was  40% more than Raeann's. If Raeann spent another $2058, she would spend the same amount of money as Anna.

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

Shiyun	Raeann	Anna
5x5	21x5
	5x21	7x21
25 u	105 u	147 u

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

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

Shiyun : Raeann
10 : 42
5 : 21

Anna's spending in percent when compared to Raeann's
= 100% + 40%
= 140%

Raeann : Anna
100 : 140
5 : 7

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

Shiyun : Raeann : Anna
25 : 105 : 147

(b)

	Shiyun	Raeann	Anna
Before	25 u	105 u	147 u
Change		+ 42 u
After	25 u	147 u	147 u

Additional amount that Raeann would have to spend to be the same as Anna
= 147 u - 105 u
= 42 u

42 u = 2058

1 u = 2058 ÷ 42 = 49

Amount that Shiyun spent
= 25 u
= 25 x 49
= $1225 

Answer(s): (a) 25 : 105 : 147; (b) $1225