Three women, Mary, Opal and Zara went on a shopping spree. 90% of Mary's spending was equal to ¹₂ of Opal's spending. Zara's spending was  25% more than Opal's. If Opal spent another $441, she would spend the same amount of money as Zara.

1. Find the ratio of Mary's spending to Opal's to Zara's.
2. How much did Mary spend?

Mary	Opal	Zara
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

910 of Mary's spending = 12 of Opal's spending
910 of Mary's spending =1x92x9 of Opal's spending
910 of Mary's spending = 918 of Opal's spending

Mary : Opal
10 : 18
5 : 9

Zara's spending in percent when compared to Opal's
= 100% + 25%
= 125%

Opal : Zara
100 : 125
4 : 5

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

Mary : Opal : Zara
20 : 36 : 45

(b)

	Mary	Opal	Zara
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 441

1 u = 441 ÷ 9 = 49

Amount that Mary spent
= 20 u
= 20 x 49
= $980 

Answer(s): (a) 20 : 36 : 45; (b) $980