Three women, Cathy, Ivory and Lucy went on a shopping spree. 90% of Cathy's spending was equal to ¹₂ of Ivory's spending. Lucy's spending was  40% less than Ivory's. If Ivory spent $954 less, she would spend the same amount of money as Lucy.

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

Cathy	Ivory	Lucy
5x5	9x5
	5x9	3x9
25 u	45 u	27 u

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

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

Cathy : Ivory
10 : 18
5 : 9

Lucy's spending in percent when compared to Ivory's
= 100% - 40%
= 60%

Ivory : Lucy
100 : 60
5 : 3

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

Cathy : Ivory : Lucy
25 : 45 : 27

(b)

	Cathy	Ivory	Lucy
Before	25 u	45 u	27 u
Change		- 18 u
After	25 u	27 u	27 u

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

18 u = 954

1 u = 954 ÷ 18 = 53

Amount that Lucy spent
= 27 u
= 27 x 53
= $1431 

Answer(s): (a) 25 : 45 : 27; (b) $1431