Three women, Ivory, Linda and Tiffany went on a shopping spree. 90% of Ivory's spending was equal to ¹₂ of Linda's spending. Tiffany's spending was  40% less than Linda's. If Linda spent $1152 less, she would spend the same amount of money as Tiffany.

1. Find the ratio of Ivory's spending to Linda's to Tiffany's.
2. How much did Tiffany spend?

Ivory	Linda	Tiffany
5x5	9x5
	5x9	3x9
25 u	45 u	27 u

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

910 of Ivory's spending = 12 of Linda's spending
910 of Ivory's spending =1x92x9 of Linda's spending
910 of Ivory's spending = 918 of Linda's spending

Ivory : Linda
10 : 18
5 : 9

Tiffany's spending in percent when compared to Linda's
= 100% - 40%
= 60%

Linda : Tiffany
100 : 60
5 : 3

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

Ivory : Linda : Tiffany
25 : 45 : 27

(b)

	Ivory	Linda	Tiffany
Before	25 u	45 u	27 u
Change		- 18 u
After	25 u	27 u	27 u

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

18 u = 1152

1 u = 1152 ÷ 18 = 64

Amount that Tiffany spent
= 27 u
= 27 x 64
= $1728 

Answer(s): (a) 25 : 45 : 27; (b) $1728