Three women, Anna, Jane and Natalie went on a shopping spree. 90% of Anna's spending was equal to ¹₆ of Jane's spending. Natalie's spending was  60% more than Jane's. If Jane spent another $8991, she would spend the same amount of money as Natalie.

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

Anna	Jane	Natalie
5x5	27x5
	5x27	8x27
25 u	135 u	216 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Anna's spending is equal to ¹₆ of Jane's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Anna's spending = 16 of Jane's spending
910 of Anna's spending =1x96x9 of Jane's spending
910 of Anna's spending = 954 of Jane's spending

Anna : Jane
10 : 54
5 : 27

Natalie's spending in percent when compared to Jane's
= 100% + 60%
= 160%

Jane : Natalie
100 : 160
5 : 8

Jane's spending is the repeated identity.  Make Jane's spending the same.  LCM of 27 and 5 is 135.

Anna : Jane : Natalie
25 : 135 : 216

(b)

	Anna	Jane	Natalie
Before	25 u	135 u	216 u
Change		+ 81 u
After	25 u	216 u	216 u

Additional amount that Jane would have to spend to be the same as Natalie
= 216 u - 135 u
= 81 u

81 u = 8991

1 u = 8991 ÷ 81 = 111

Amount that Anna spent
= 25 u
= 25 x 111
= $2775 

Answer(s): (a) 25 : 135 : 216; (b) $2775