Three women, Jean, Roshel and Winnie went on a shopping spree. 70% of Jean's spending was equal to ¹₆ of Roshel's spending. Winnie's spending was  40% less than Roshel's. If Roshel spent $1386 less, she would spend the same amount of money as Winnie.

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

Jean	Roshel	Winnie
5x5	21x5
	5x21	3x21
25 u	105 u	63 u

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

710 of Jean's spending = 16 of Roshel's spending
710 of Jean's spending =1x76x7 of Roshel's spending
710 of Jean's spending = 742 of Roshel's spending

Jean : Roshel
10 : 42
5 : 21

Winnie's spending in percent when compared to Roshel's
= 100% - 40%
= 60%

Roshel : Winnie
100 : 60
5 : 3

Roshel's spending is the repeated identity.  Make Roshel's spending the same.  LCM of 21 and 5 is 105.

Jean : Roshel : Winnie
25 : 105 : 63

(b)

	Jean	Roshel	Winnie
Before	25 u	105 u	63 u
Change		- 42 u
After	25 u	63 u	63 u

Additional amount that Roshel would have to spend less to be the same as Winnie
= 105 u - 63 u
= 42 u

42 u = 1386

1 u = 1386 ÷ 42 = 33

Amount that Winnie spent
= 63 u
= 63 x 33
= $2079 

Answer(s): (a) 25 : 105 : 63; (b) $2079