Three women, Mary, Anna and Tiffany went on a shopping spree. 90% of Mary's spending was equal to ¹₅ of Anna's spending. Tiffany's spending was  25% more than Anna's. If Anna spent another $450, she would spend the same amount of money as Tiffany.

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

Mary	Anna	Tiffany
2x4	9x4
	4x9	5x9
8 u	36 u	45 u

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

910 of Mary's spending = 15 of Anna's spending
910 of Mary's spending =1x95x9 of Anna's spending
910 of Mary's spending = 945 of Anna's spending

Mary : Anna
10 : 45
2 : 9

Tiffany's spending in percent when compared to Anna's
= 100% + 25%
= 125%

Anna : Tiffany
100 : 125
4 : 5

Anna's spending is the repeated identity.  Make Anna's spending the same.  LCM of 9 and 4 is 36.

Mary : Anna : Tiffany
8 : 36 : 45

(b)

	Mary	Anna	Tiffany
Before	8 u	36 u	45 u
Change		+ 9 u
After	8 u	45 u	45 u

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

9 u = 450

1 u = 450 ÷ 9 = 50

Amount that Mary spent
= 8 u
= 8 x 50
= $400 

Answer(s): (a) 8 : 36 : 45; (b) $400