Three women, Kathy, Fiona and Nora went on a shopping spree. 30% of Kathy's spending was equal to ¹₆ of Fiona's spending. Nora's spending was  25% more than Fiona's. If Fiona spent another $963, she would spend the same amount of money as Nora.

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

Kathy	Fiona	Nora
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Kathy's spending is equal to ¹₆ of Fiona's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Kathy's spending = 16 of Fiona's spending
310 of Kathy's spending =1x36x3 of Fiona's spending
310 of Kathy's spending = 318 of Fiona's spending

Kathy : Fiona
10 : 18
5 : 9

Nora's spending in percent when compared to Fiona's
= 100% + 25%
= 125%

Fiona : Nora
100 : 125
4 : 5

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

Kathy : Fiona : Nora
20 : 36 : 45

(b)

	Kathy	Fiona	Nora
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 963

1 u = 963 ÷ 9 = 107

Amount that Kathy spent
= 20 u
= 20 x 107
= $2140 

Answer(s): (a) 20 : 36 : 45; (b) $2140