Three women, Yoko, Pamela and Xandra went on a shopping spree. 90% of Yoko's spending was equal to ¹₂ of Pamela's spending. Xandra's spending was  25% more than Pamela's. If Pamela spent another $1071, she would spend the same amount of money as Xandra.

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

Yoko	Pamela	Xandra
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

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

Yoko : Pamela
10 : 18
5 : 9

Xandra's spending in percent when compared to Pamela's
= 100% + 25%
= 125%

Pamela : Xandra
100 : 125
4 : 5

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

Yoko : Pamela : Xandra
20 : 36 : 45

(b)

	Yoko	Pamela	Xandra
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 1071

1 u = 1071 ÷ 9 = 119

Amount that Yoko spent
= 20 u
= 20 x 119
= $2380 

Answer(s): (a) 20 : 36 : 45; (b) $2380