Three women, Hazel, Shiyun and Joelle went on a shopping spree. 70% of Hazel's spending was equal to ¹₂ of Shiyun's spending. Joelle's spending was  80% less than Shiyun's. If Shiyun spent $588 less, she would spend the same amount of money as Joelle.

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

Hazel	Shiyun	Joelle
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Hazel's spending is equal to ¹₂ of Shiyun's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Hazel's spending = 12 of Shiyun's spending
710 of Hazel's spending =1x72x7 of Shiyun's spending
710 of Hazel's spending = 714 of Shiyun's spending

Hazel : Shiyun
10 : 14
5 : 7

Joelle's spending in percent when compared to Shiyun's
= 100% - 80%
= 20%

Shiyun : Joelle
100 : 20
5 : 1

Shiyun's spending is the repeated identity.  Make Shiyun's spending the same.  LCM of 7 and 5 is 35.

Hazel : Shiyun : Joelle
25 : 35 : 7

(b)

	Hazel	Shiyun	Joelle
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

Additional amount that Shiyun would have to spend less to be the same as Joelle
= 35 u - 7 u
= 28 u

28 u = 588

1 u = 588 ÷ 28 = 21

Amount that Joelle spent
= 7 u
= 7 x 21
= $147 

Answer(s): (a) 25 : 35 : 7; (b) $147