Three women, Kathy, Nora and Tina went on a shopping spree. 90% of Kathy's spending was equal to ¹₂ of Nora's spending. Tina's spending was  40% more than Nora's. If Nora spent another $774, she would spend the same amount of money as Tina.

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

Kathy	Nora	Tina
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Kathy's spending is equal to ¹₂ of Nora's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Kathy's spending = 12 of Nora's spending
910 of Kathy's spending =1x92x9 of Nora's spending
910 of Kathy's spending = 918 of Nora's spending

Kathy : Nora
10 : 18
5 : 9

Tina's spending in percent when compared to Nora's
= 100% + 40%
= 140%

Nora : Tina
100 : 140
5 : 7

Nora's spending is the repeated identity.  Make Nora's spending the same.  LCM of 9 and 5 is 45.

Kathy : Nora : Tina
25 : 45 : 63

(b)

	Kathy	Nora	Tina
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Nora would have to spend to be the same as Tina
= 63 u - 45 u
= 18 u

18 u = 774

1 u = 774 ÷ 18 = 43

Amount that Kathy spent
= 25 u
= 25 x 43
= $1075 

Answer(s): (a) 25 : 45 : 63; (b) $1075