Three women, Raeann, Mary and Kathy went on a shopping spree. 90% of Raeann's spending was equal to ¹₆ of Mary's spending. Kathy's spending was  60% less than Mary's. If Mary spent $9558 less, she would spend the same amount of money as Kathy.

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

Raeann	Mary	Kathy
5x5	27x5
	5x27	2x27
25 u	135 u	54 u

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

910 of Raeann's spending = 16 of Mary's spending
910 of Raeann's spending =1x96x9 of Mary's spending
910 of Raeann's spending = 954 of Mary's spending

Raeann : Mary
10 : 54
5 : 27

Kathy's spending in percent when compared to Mary's
= 100% - 60%
= 40%

Mary : Kathy
100 : 40
5 : 2

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

Raeann : Mary : Kathy
25 : 135 : 54

(b)

	Raeann	Mary	Kathy
Before	25 u	135 u	54 u
Change		- 81 u
After	25 u	54 u	54 u

Additional amount that Mary would have to spend less to be the same as Kathy
= 135 u - 54 u
= 81 u

81 u = 9558

1 u = 9558 ÷ 81 = 118

Amount that Kathy spent
= 54 u
= 54 x 118
= $6372 

Answer(s): (a) 25 : 135 : 54; (b) $6372