Three women, Jane, Diana and Pamela went on a shopping spree. 90% of Jane's spending was equal to ¹₅ of Diana's spending. Pamela's spending was  60% more than Diana's. If Diana spent another $1836, she would spend the same amount of money as Pamela.

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

Jane	Diana	Pamela
2x5	9x5
	5x9	8x9
10 u	45 u	72 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Jane's spending is equal to ¹₅ of Diana's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Jane's spending = 15 of Diana's spending
910 of Jane's spending =1x95x9 of Diana's spending
910 of Jane's spending = 945 of Diana's spending

Jane : Diana
10 : 45
2 : 9

Pamela's spending in percent when compared to Diana's
= 100% + 60%
= 160%

Diana : Pamela
100 : 160
5 : 8

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

Jane : Diana : Pamela
10 : 45 : 72

(b)

	Jane	Diana	Pamela
Before	10 u	45 u	72 u
Change		+ 27 u
After	10 u	72 u	72 u

Additional amount that Diana would have to spend to be the same as Pamela
= 72 u - 45 u
= 27 u

27 u = 1836

1 u = 1836 ÷ 27 = 68

Amount that Jane spent
= 10 u
= 10 x 68
= $680 

Answer(s): (a) 10 : 45 : 72; (b) $680