Three women, Fanny, Lucy and Ivory went on a shopping spree. 70% of Fanny's spending was equal to ¹₆ of Lucy's spending. Ivory's spending was  70% less than Lucy's. If Lucy spent $3528 less, she would spend the same amount of money as Ivory.

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

Fanny	Lucy	Ivory
5x10	21x10
	10x21	3x21
50 u	210 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Fanny's spending is equal to ¹₆ of Lucy's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Fanny's spending = 16 of Lucy's spending
710 of Fanny's spending =1x76x7 of Lucy's spending
710 of Fanny's spending = 742 of Lucy's spending

Fanny : Lucy
10 : 42
5 : 21

Ivory's spending in percent when compared to Lucy's
= 100% - 70%
= 30%

Lucy : Ivory
100 : 30
10 : 3

Lucy's spending is the repeated identity.  Make Lucy's spending the same.  LCM of 21 and 10 is 210.

Fanny : Lucy : Ivory
50 : 210 : 63

(b)

	Fanny	Lucy	Ivory
Before	50 u	210 u	63 u
Change		- 147 u
After	50 u	63 u	63 u

Additional amount that Lucy would have to spend less to be the same as Ivory
= 210 u - 63 u
= 147 u

147 u = 3528

1 u = 3528 ÷ 147 = 24

Amount that Ivory spent
= 63 u
= 63 x 24
= $1512 

Answer(s): (a) 50 : 210 : 63; (b) $1512