Three women, Shiyun, Gwen and Cathy went on a shopping spree. 30% of Shiyun's spending was equal to ¹₅ of Gwen's spending. Cathy's spending was  40% more than Gwen's. If Gwen spent another $492, she would spend the same amount of money as Cathy.

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

Shiyun	Gwen	Cathy
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Shiyun's spending is equal to ¹₅ of Gwen's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Shiyun's spending = 15 of Gwen's spending
310 of Shiyun's spending =1x35x3 of Gwen's spending
310 of Shiyun's spending = 315 of Gwen's spending

Shiyun : Gwen
10 : 15
2 : 3

Cathy's spending in percent when compared to Gwen's
= 100% + 40%
= 140%

Gwen : Cathy
100 : 140
5 : 7

Gwen's spending is the repeated identity.  Make Gwen's spending the same.  LCM of 3 and 5 is 15.

Shiyun : Gwen : Cathy
10 : 15 : 21

(b)

	Shiyun	Gwen	Cathy
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Gwen would have to spend to be the same as Cathy
= 21 u - 15 u
= 6 u

6 u = 492

1 u = 492 ÷ 6 = 82

Amount that Shiyun spent
= 10 u
= 10 x 82
= $820 

Answer(s): (a) 10 : 15 : 21; (b) $820