Three women, Diana, Kimberly and Jade went on a shopping spree. 30% of Diana's spending was equal to ¹₆ of Kimberly's spending. Jade's spending was  40% more than Kimberly's. If Kimberly spent another $432, she would spend the same amount of money as Jade.

1. Find the ratio of Diana's spending to Kimberly's to Jade's.
2. How much did Diana spend?

Diana	Kimberly	Jade
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

310 of Diana's spending = 16 of Kimberly's spending
310 of Diana's spending =1x36x3 of Kimberly's spending
310 of Diana's spending = 318 of Kimberly's spending

Diana : Kimberly
10 : 18
5 : 9

Jade's spending in percent when compared to Kimberly's
= 100% + 40%
= 140%

Kimberly : Jade
100 : 140
5 : 7

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

Diana : Kimberly : Jade
25 : 45 : 63

(b)

	Diana	Kimberly	Jade
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 432

1 u = 432 ÷ 18 = 24

Amount that Diana spent
= 25 u
= 25 x 24
= $600 

Answer(s): (a) 25 : 45 : 63; (b) $600