Three women, Vanessa, Erika and Hazel went on a shopping spree. 90% of Vanessa's spending was equal to ¹₂ of Erika's spending. Hazel's spending was  60% more than Erika's. If Erika spent another $702, she would spend the same amount of money as Hazel.

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

Vanessa	Erika	Hazel
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

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

910 of Vanessa's spending = 12 of Erika's spending
910 of Vanessa's spending =1x92x9 of Erika's spending
910 of Vanessa's spending = 918 of Erika's spending

Vanessa : Erika
10 : 18
5 : 9

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

Erika : Hazel
100 : 160
5 : 8

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

Vanessa : Erika : Hazel
25 : 45 : 72

(b)

	Vanessa	Erika	Hazel
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

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

27 u = 702

1 u = 702 ÷ 27 = 26

Amount that Vanessa spent
= 25 u
= 25 x 26
= $650 

Answer(s): (a) 25 : 45 : 72; (b) $650