Three women, Usha, Risa and Opal went on a shopping spree. 90% of Usha's spending was equal to ¹₂ of Risa's spending. Opal's spending was  25% more than Risa's. If Risa spent another $891, she would spend the same amount of money as Opal.

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

Usha	Risa	Opal
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

910 of Usha's spending = 12 of Risa's spending
910 of Usha's spending =1x92x9 of Risa's spending
910 of Usha's spending = 918 of Risa's spending

Usha : Risa
10 : 18
5 : 9

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

Risa : Opal
100 : 125
4 : 5

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

Usha : Risa : Opal
20 : 36 : 45

(b)

	Usha	Risa	Opal
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 891

1 u = 891 ÷ 9 = 99

Amount that Usha spent
= 20 u
= 20 x 99
= $1980 

Answer(s): (a) 20 : 36 : 45; (b) $1980