Three women, Ivory, Min and Gwen went on a shopping spree. 90% of Ivory's spending was equal to ¹₅ of Min's spending. Gwen's spending was  25% more than Min's. If Min spent another $810, she would spend the same amount of money as Gwen.

1. Find the ratio of Ivory's spending to Min's to Gwen's.
2. How much did Ivory spend?

Ivory	Min	Gwen
2x4	9x4
	4x9	5x9
8 u	36 u	45 u

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

910 of Ivory's spending = 15 of Min's spending
910 of Ivory's spending =1x95x9 of Min's spending
910 of Ivory's spending = 945 of Min's spending

Ivory : Min
10 : 45
2 : 9

Gwen's spending in percent when compared to Min's
= 100% + 25%
= 125%

Min : Gwen
100 : 125
4 : 5

Min's spending is the repeated identity.  Make Min's spending the same.  LCM of 9 and 4 is 36.

Ivory : Min : Gwen
8 : 36 : 45

(b)

	Ivory	Min	Gwen
Before	8 u	36 u	45 u
Change		+ 9 u
After	8 u	45 u	45 u

Additional amount that Min would have to spend to be the same as Gwen
= 45 u - 36 u
= 9 u

9 u = 810

1 u = 810 ÷ 9 = 90

Amount that Ivory spent
= 8 u
= 8 x 90
= $720 

Answer(s): (a) 8 : 36 : 45; (b) $720