Three women, Xandra, Esther and Jade went on a shopping spree. 90% of Xandra's spending was equal to ¹₂ of Esther's spending. Jade's spending was  80% less than Esther's. If Esther spent $2880 less, she would spend the same amount of money as Jade.

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

Xandra	Esther	Jade
5x5	9x5
	5x9	1x9
25 u	45 u	9 u

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

910 of Xandra's spending = 12 of Esther's spending
910 of Xandra's spending =1x92x9 of Esther's spending
910 of Xandra's spending = 918 of Esther's spending

Xandra : Esther
10 : 18
5 : 9

Jade's spending in percent when compared to Esther's
= 100% - 80%
= 20%

Esther : Jade
100 : 20
5 : 1

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

Xandra : Esther : Jade
25 : 45 : 9

(b)

	Xandra	Esther	Jade
Before	25 u	45 u	9 u
Change		- 36 u
After	25 u	9 u	9 u

Additional amount that Esther would have to spend less to be the same as Jade
= 45 u - 9 u
= 36 u

36 u = 2880

1 u = 2880 ÷ 36 = 80

Amount that Jade spent
= 9 u
= 9 x 80
= $720 

Answer(s): (a) 25 : 45 : 9; (b) $720