Three women, Joelle, Linda and Xylia went on a shopping spree. 90% of Joelle's spending was equal to ¹₆ of Linda's spending. Xylia's spending was  40% more than Linda's. If Linda spent another $1080, she would spend the same amount of money as Xylia.

1. Find the ratio of Joelle's spending to Linda's to Xylia's.
2. How much did Joelle spend?

Joelle	Linda	Xylia
5x5	27x5
	5x27	7x27
25 u	135 u	189 u

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

910 of Joelle's spending = 16 of Linda's spending
910 of Joelle's spending =1x96x9 of Linda's spending
910 of Joelle's spending = 954 of Linda's spending

Joelle : Linda
10 : 54
5 : 27

Xylia's spending in percent when compared to Linda's
= 100% + 40%
= 140%

Linda : Xylia
100 : 140
5 : 7

Linda's spending is the repeated identity.  Make Linda's spending the same.  LCM of 27 and 5 is 135.

Joelle : Linda : Xylia
25 : 135 : 189

(b)

	Joelle	Linda	Xylia
Before	25 u	135 u	189 u
Change		+ 54 u
After	25 u	189 u	189 u

Additional amount that Linda would have to spend to be the same as Xylia
= 189 u - 135 u
= 54 u

54 u = 1080

1 u = 1080 ÷ 54 = 20

Amount that Joelle spent
= 25 u
= 25 x 20
= $500 

Answer(s): (a) 25 : 135 : 189; (b) $500