Three women, Jaslyn, Shiyun and Risa went on a shopping spree. 30% of Jaslyn's spending was equal to ¹₆ of Shiyun's spending. Risa's spending was  25% less than Shiyun's. If Shiyun spent $180 less, she would spend the same amount of money as Risa.

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

Jaslyn	Shiyun	Risa
5x4	9x4
	4x9	3x9
20 u	36 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Jaslyn's spending is equal to ¹₆ of Shiyun's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Jaslyn's spending = 16 of Shiyun's spending
310 of Jaslyn's spending =1x36x3 of Shiyun's spending
310 of Jaslyn's spending = 318 of Shiyun's spending

Jaslyn : Shiyun
10 : 18
5 : 9

Risa's spending in percent when compared to Shiyun's
= 100% - 25%
= 75%

Shiyun : Risa
100 : 75
4 : 3

Shiyun's spending is the repeated identity.  Make Shiyun's spending the same.  LCM of 9 and 4 is 36.

Jaslyn : Shiyun : Risa
20 : 36 : 27

(b)

	Jaslyn	Shiyun	Risa
Before	20 u	36 u	27 u
Change		- 9 u
After	20 u	27 u	27 u

Additional amount that Shiyun would have to spend less to be the same as Risa
= 36 u - 27 u
= 9 u

9 u = 180

1 u = 180 ÷ 9 = 20

Amount that Risa spent
= 27 u
= 27 x 20
= $540 

Answer(s): (a) 20 : 36 : 27; (b) $540