Three women, Yen, Gabby and Eva went on a shopping spree. 90% of Yen's spending was equal to ¹₅ of Gabby's spending. Eva's spending was  50% more than Gabby's. If Gabby spent another $1080, she would spend the same amount of money as Eva.

1. Find the ratio of Yen's spending to Gabby's to Eva's.
2. How much did Yen spend?

Yen	Gabby	Eva
2x2	9x2
	2x9	3x9
4 u	18 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Yen's spending is equal to ¹₅ of Gabby's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Yen's spending = 15 of Gabby's spending
910 of Yen's spending =1x95x9 of Gabby's spending
910 of Yen's spending = 945 of Gabby's spending

Yen : Gabby
10 : 45
2 : 9

Eva's spending in percent when compared to Gabby's
= 100% + 50%
= 150%

Gabby : Eva
100 : 150
2 : 3

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

Yen : Gabby : Eva
4 : 18 : 27

(b)

	Yen	Gabby	Eva
Before	4 u	18 u	27 u
Change		+ 9 u
After	4 u	27 u	27 u

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

9 u = 1080

1 u = 1080 ÷ 9 = 120

Amount that Yen spent
= 4 u
= 4 x 120
= $480 

Answer(s): (a) 4 : 18 : 27; (b) $480