Three women, Pamela, Nora and Yoko went on a shopping spree. 90% of Pamela's spending was equal to ¹₆ of Nora's spending. Yoko's spending was  70% less than Nora's. If Nora spent $19467 less, she would spend the same amount of money as Yoko.

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

Pamela	Nora	Yoko
5x10	27x10
	10x27	3x27
50 u	270 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Pamela's spending is equal to ¹₆ of Nora's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Pamela's spending = 16 of Nora's spending
910 of Pamela's spending =1x96x9 of Nora's spending
910 of Pamela's spending = 954 of Nora's spending

Pamela : Nora
10 : 54
5 : 27

Yoko's spending in percent when compared to Nora's
= 100% - 70%
= 30%

Nora : Yoko
100 : 30
10 : 3

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

Pamela : Nora : Yoko
50 : 270 : 81

(b)

	Pamela	Nora	Yoko
Before	50 u	270 u	81 u
Change		- 189 u
After	50 u	81 u	81 u

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

189 u = 19467

1 u = 19467 ÷ 189 = 103

Amount that Yoko spent
= 81 u
= 81 x 103
= $8343 

Answer(s): (a) 50 : 270 : 81; (b) $8343