Three women, Risa, Julie and Hilda went on a shopping spree. 90% of Risa's spending was equal to ¹₂ of Julie's spending. Hilda's spending was  40% more than Julie's. If Julie spent another $2160, she would spend the same amount of money as Hilda.

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

Risa	Julie	Hilda
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

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

Risa : Julie
10 : 18
5 : 9

Hilda's spending in percent when compared to Julie's
= 100% + 40%
= 140%

Julie : Hilda
100 : 140
5 : 7

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

Risa : Julie : Hilda
25 : 45 : 63

(b)

	Risa	Julie	Hilda
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Julie would have to spend to be the same as Hilda
= 63 u - 45 u
= 18 u

18 u = 2160

1 u = 2160 ÷ 18 = 120

Amount that Risa spent
= 25 u
= 25 x 120
= $3000 

Answer(s): (a) 25 : 45 : 63; (b) $3000