Three women, Raeann, Mary and Linda went on a shopping spree. 90% of Raeann's spending was equal to ¹₆ of Mary's spending. Linda's spending was  70% less than Mary's. If Mary spent $4536 less, she would spend the same amount of money as Linda.

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

Raeann	Mary	Linda
5x10	27x10
	10x27	3x27
50 u	270 u	81 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

Linda's spending in percent when compared to Mary's
= 100% - 70%
= 30%

Mary : Linda
100 : 30
10 : 3

Mary's spending is the repeated identity.  Make Mary's spending the same.  LCM of 27 and 10 is 270.

Raeann : Mary : Linda
50 : 270 : 81

(b)

	Raeann	Mary	Linda
Before	50 u	270 u	81 u
Change		- 189 u
After	50 u	81 u	81 u

Additional amount that Mary would have to spend less to be the same as Linda
= 270 u - 81 u
= 189 u

189 u = 4536

1 u = 4536 ÷ 189 = 24

Amount that Linda spent
= 81 u
= 81 x 24
= $1944 

Answer(s): (a) 50 : 270 : 81; (b) $1944