Three women, Fiona, Mary and Risa went on a shopping spree. 30% of Fiona's spending was equal to ¹₂ of Mary's spending. Risa's spending was  60% more than Mary's. If Mary spent another $522, she would spend the same amount of money as Risa.

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

Fiona	Mary	Risa
5x5	3x5
	5x3	8x3
25 u	15 u	24 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Fiona's spending is equal to ¹₂ of Mary's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Fiona's spending = 12 of Mary's spending
310 of Fiona's spending =1x32x3 of Mary's spending
310 of Fiona's spending = 36 of Mary's spending

Fiona : Mary
10 : 6
5 : 3

Risa's spending in percent when compared to Mary's
= 100% + 60%
= 160%

Mary : Risa
100 : 160
5 : 8

Mary's spending is the repeated identity.  Make Mary's spending the same.  LCM of 3 and 5 is 15.

Fiona : Mary : Risa
25 : 15 : 24

(b)

	Fiona	Mary	Risa
Before	25 u	15 u	24 u
Change		+ 9 u
After	25 u	24 u	24 u

Additional amount that Mary would have to spend to be the same as Risa
= 24 u - 15 u
= 9 u

9 u = 522

1 u = 522 ÷ 9 = 58

Amount that Fiona spent
= 25 u
= 25 x 58
= $1450 

Answer(s): (a) 25 : 15 : 24; (b) $1450