Three women, Jane, Diana and Anna went on a shopping spree. 90% of Jane's spending was equal to ¹₅ of Diana's spending. Anna's spending was  80% less than Diana's. If Diana spent $3060 less, she would spend the same amount of money as Anna.

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

Jane	Diana	Anna
2x5	9x5
	5x9	1x9
10 u	45 u	9 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

Anna's spending in percent when compared to Diana's
= 100% - 80%
= 20%

Diana : Anna
100 : 20
5 : 1

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

Jane : Diana : Anna
10 : 45 : 9

(b)

	Jane	Diana	Anna
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

Additional amount that Diana would have to spend less to be the same as Anna
= 45 u - 9 u
= 36 u

36 u = 3060

1 u = 3060 ÷ 36 = 85

Amount that Anna spent
= 9 u
= 9 x 85
= $765 

Answer(s): (a) 10 : 45 : 9; (b) $765