Three women, Pamela, Vanessa and Cindy went on a shopping spree. 30% of Pamela's spending was equal to ¹₆ of Vanessa's spending. Cindy's spending was  70% less than Vanessa's. If Vanessa spent $3843 less, she would spend the same amount of money as Cindy.

1. Find the ratio of Pamela's spending to Vanessa's to Cindy's.
2. How much did Cindy spend?

Pamela	Vanessa	Cindy
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

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

310 of Pamela's spending = 16 of Vanessa's spending
310 of Pamela's spending =1x36x3 of Vanessa's spending
310 of Pamela's spending = 318 of Vanessa's spending

Pamela : Vanessa
10 : 18
5 : 9

Cindy's spending in percent when compared to Vanessa's
= 100% - 70%
= 30%

Vanessa : Cindy
100 : 30
10 : 3

Vanessa's spending is the repeated identity.  Make Vanessa's spending the same.  LCM of 9 and 10 is 90.

Pamela : Vanessa : Cindy
50 : 90 : 27

(b)

	Pamela	Vanessa	Cindy
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Vanessa would have to spend less to be the same as Cindy
= 90 u - 27 u
= 63 u

63 u = 3843

1 u = 3843 ÷ 63 = 61

Amount that Cindy spent
= 27 u
= 27 x 61
= $1647 

Answer(s): (a) 50 : 90 : 27; (b) $1647