Three women, Diana, Cathy and Erika went on a shopping spree. 90% of Diana's spending was equal to ¹₂ of Cathy's spending. Erika's spending was  40% more than Cathy's. If Cathy spent another $1440, she would spend the same amount of money as Erika.

1. Find the ratio of Diana's spending to Cathy's to Erika's.
2. How much did Diana spend?

Diana	Cathy	Erika
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

910 of Diana's spending = 12 of Cathy's spending
910 of Diana's spending =1x92x9 of Cathy's spending
910 of Diana's spending = 918 of Cathy's spending

Diana : Cathy
10 : 18
5 : 9

Erika's spending in percent when compared to Cathy's
= 100% + 40%
= 140%

Cathy : Erika
100 : 140
5 : 7

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

Diana : Cathy : Erika
25 : 45 : 63

(b)

	Diana	Cathy	Erika
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 1440

1 u = 1440 ÷ 18 = 80

Amount that Diana spent
= 25 u
= 25 x 80
= $2000 

Answer(s): (a) 25 : 45 : 63; (b) $2000