Three women, Yoko, Nora and Shannon went on a shopping spree. 90% of Yoko's spending was equal to ¹₂ of Nora's spending. Shannon's spending was  50% more than Nora's. If Nora spent another $360, she would spend the same amount of money as Shannon.

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

Yoko	Nora	Shannon
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

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

Yoko : Nora
10 : 18
5 : 9

Shannon's spending in percent when compared to Nora's
= 100% + 50%
= 150%

Nora : Shannon
100 : 150
2 : 3

Nora's spending is the repeated identity.  Make Nora's spending the same.  LCM of 9 and 2 is 18.

Yoko : Nora : Shannon
10 : 18 : 27

(b)

	Yoko	Nora	Shannon
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Nora would have to spend to be the same as Shannon
= 27 u - 18 u
= 9 u

9 u = 360

1 u = 360 ÷ 9 = 40

Amount that Yoko spent
= 10 u
= 10 x 40
= $400 

Answer(s): (a) 10 : 18 : 27; (b) $400