Three women, Winnie, Linda and Natalie went on a shopping spree. 70% of Winnie's spending was equal to ¹₅ of Linda's spending. Natalie's spending was  80% less than Linda's. If Linda spent $1680 less, she would spend the same amount of money as Natalie.

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

Winnie	Linda	Natalie
2x5	7x5
	5x7	1x7
10 u	35 u	7 u

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

710 of Winnie's spending = 15 of Linda's spending
710 of Winnie's spending =1x75x7 of Linda's spending
710 of Winnie's spending = 735 of Linda's spending

Winnie : Linda
10 : 35
2 : 7

Natalie's spending in percent when compared to Linda's
= 100% - 80%
= 20%

Linda : Natalie
100 : 20
5 : 1

Linda's spending is the repeated identity.  Make Linda's spending the same.  LCM of 7 and 5 is 35.

Winnie : Linda : Natalie
10 : 35 : 7

(b)

	Winnie	Linda	Natalie
Before	10 u	35 u	7 u
Change		- 28 u
After	10 u	7 u	7 u

Additional amount that Linda would have to spend less to be the same as Natalie
= 35 u - 7 u
= 28 u

28 u = 1680

1 u = 1680 ÷ 28 = 60

Amount that Natalie spent
= 7 u
= 7 x 60
= $420 

Answer(s): (a) 10 : 35 : 7; (b) $420