Three women, Kathy, Pamela and Betty went on a shopping spree. 30% of Kathy's spending was equal to ¹₆ of Pamela's spending. Betty's spending was  40% more than Pamela's. If Pamela spent another $540, she would spend the same amount of money as Betty.

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

Kathy	Pamela	Betty
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

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

Kathy : Pamela
10 : 18
5 : 9

Betty's spending in percent when compared to Pamela's
= 100% + 40%
= 140%

Pamela : Betty
100 : 140
5 : 7

Pamela's spending is the repeated identity.  Make Pamela's spending the same.  LCM of 9 and 5 is 45.

Kathy : Pamela : Betty
25 : 45 : 63

(b)

	Kathy	Pamela	Betty
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Pamela would have to spend to be the same as Betty
= 63 u - 45 u
= 18 u

18 u = 540

1 u = 540 ÷ 18 = 30

Amount that Kathy spent
= 25 u
= 25 x 30
= $750 

Answer(s): (a) 25 : 45 : 63; (b) $750