Three women, Opal, Usha and Hilda went on a shopping spree. 90% of Opal's spending was equal to ¹₂ of Usha's spending. Hilda's spending was  60% less than Usha's. If Usha spent $2187 less, she would spend the same amount of money as Hilda.

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

Opal	Usha	Hilda
5x5	9x5
	5x9	2x9
25 u	45 u	18 u

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

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

Opal : Usha
10 : 18
5 : 9

Hilda's spending in percent when compared to Usha's
= 100% - 60%
= 40%

Usha : Hilda
100 : 40
5 : 2

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

Opal : Usha : Hilda
25 : 45 : 18

(b)

	Opal	Usha	Hilda
Before	25 u	45 u	18 u
Change		- 27 u
After	25 u	18 u	18 u

Additional amount that Usha would have to spend less to be the same as Hilda
= 45 u - 18 u
= 27 u

27 u = 2187

1 u = 2187 ÷ 27 = 81

Amount that Hilda spent
= 18 u
= 18 x 81
= $1458 

Answer(s): (a) 25 : 45 : 18; (b) $1458