Three women, Gwen, Lucy and Irene went on a shopping spree. 70% of Gwen's spending was equal to ¹₅ of Lucy's spending. Irene's spending was  25% less than Lucy's. If Lucy spent $280 less, she would spend the same amount of money as Irene.

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

Gwen	Lucy	Irene
2x4	7x4
	4x7	3x7
8 u	28 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Gwen's spending is equal to ¹₅ of Lucy's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Gwen's spending = 15 of Lucy's spending
710 of Gwen's spending =1x75x7 of Lucy's spending
710 of Gwen's spending = 735 of Lucy's spending

Gwen : Lucy
10 : 35
2 : 7

Irene's spending in percent when compared to Lucy's
= 100% - 25%
= 75%

Lucy : Irene
100 : 75
4 : 3

Lucy's spending is the repeated identity.  Make Lucy's spending the same.  LCM of 7 and 4 is 28.

Gwen : Lucy : Irene
8 : 28 : 21

(b)

	Gwen	Lucy	Irene
Before	8 u	28 u	21 u
Change		- 7 u
After	8 u	21 u	21 u

Additional amount that Lucy would have to spend less to be the same as Irene
= 28 u - 21 u
= 7 u

7 u = 280

1 u = 280 ÷ 7 = 40

Amount that Irene spent
= 21 u
= 21 x 40
= $840 

Answer(s): (a) 8 : 28 : 21; (b) $840