Three women, Gabby, Hazel and Dana went on a shopping spree. 90% of Gabby's spending was equal to ¹₅ of Hazel's spending. Dana's spending was  60% more than Hazel's. If Hazel spent another $1836, she would spend the same amount of money as Dana.

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

Gabby	Hazel	Dana
2x5	9x5
	5x9	8x9
10 u	45 u	72 u

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

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

Gabby : Hazel
10 : 45
2 : 9

Dana's spending in percent when compared to Hazel's
= 100% + 60%
= 160%

Hazel : Dana
100 : 160
5 : 8

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

Gabby : Hazel : Dana
10 : 45 : 72

(b)

	Gabby	Hazel	Dana
Before	10 u	45 u	72 u
Change		+ 27 u
After	10 u	72 u	72 u

Additional amount that Hazel would have to spend to be the same as Dana
= 72 u - 45 u
= 27 u

27 u = 1836

1 u = 1836 ÷ 27 = 68

Amount that Gabby spent
= 10 u
= 10 x 68
= $680 

Answer(s): (a) 10 : 45 : 72; (b) $680