Three women, Kylie, Sabrina and Shiyun went on a shopping spree. 70% of Kylie's spending was equal to ¹₆ of Sabrina's spending. Shiyun's spending was  40% more than Sabrina's. If Sabrina spent another $4116, she would spend the same amount of money as Shiyun.

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

Kylie	Sabrina	Shiyun
5x5	21x5
	5x21	7x21
25 u	105 u	147 u

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

710 of Kylie's spending = 16 of Sabrina's spending
710 of Kylie's spending =1x76x7 of Sabrina's spending
710 of Kylie's spending = 742 of Sabrina's spending

Kylie : Sabrina
10 : 42
5 : 21

Shiyun's spending in percent when compared to Sabrina's
= 100% + 40%
= 140%

Sabrina : Shiyun
100 : 140
5 : 7

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

Kylie : Sabrina : Shiyun
25 : 105 : 147

(b)

	Kylie	Sabrina	Shiyun
Before	25 u	105 u	147 u
Change		+ 42 u
After	25 u	147 u	147 u

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

42 u = 4116

1 u = 4116 ÷ 42 = 98

Amount that Kylie spent
= 25 u
= 25 x 98
= $2450 

Answer(s): (a) 25 : 105 : 147; (b) $2450