Three women, Cindy, Jane and Lucy went on a shopping spree. 30% of Cindy's spending was equal to ¹₆ of Jane's spending. Lucy's spending was  80% less than Jane's. If Jane spent $1440 less, she would spend the same amount of money as Lucy.

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

Cindy	Jane	Lucy
5x5	9x5
	5x9	1x9
25 u	45 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Cindy's spending is equal to ¹₆ of Jane's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Cindy's spending = 16 of Jane's spending
310 of Cindy's spending =1x36x3 of Jane's spending
310 of Cindy's spending = 318 of Jane's spending

Cindy : Jane
10 : 18
5 : 9

Lucy's spending in percent when compared to Jane's
= 100% - 80%
= 20%

Jane : Lucy
100 : 20
5 : 1

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

Cindy : Jane : Lucy
25 : 45 : 9

(b)

	Cindy	Jane	Lucy
Before	25 u	45 u	9 u
Change		- 36 u
After	25 u	9 u	9 u

Additional amount that Jane would have to spend less to be the same as Lucy
= 45 u - 9 u
= 36 u

36 u = 1440

1 u = 1440 ÷ 36 = 40

Amount that Lucy spent
= 9 u
= 9 x 40
= $360 

Answer(s): (a) 25 : 45 : 9; (b) $360