Three women, Irene, Sarah and Raeann went on a shopping spree. 70% of Irene's spending was equal to ¹₆ of Sarah's spending. Raeann's spending was  40% less than Sarah's. If Sarah spent $1302 less, she would spend the same amount of money as Raeann.

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

Irene	Sarah	Raeann
5x5	21x5
	5x21	3x21
25 u	105 u	63 u

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

710 of Irene's spending = 16 of Sarah's spending
710 of Irene's spending =1x76x7 of Sarah's spending
710 of Irene's spending = 742 of Sarah's spending

Irene : Sarah
10 : 42
5 : 21

Raeann's spending in percent when compared to Sarah's
= 100% - 40%
= 60%

Sarah : Raeann
100 : 60
5 : 3

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

Irene : Sarah : Raeann
25 : 105 : 63

(b)

	Irene	Sarah	Raeann
Before	25 u	105 u	63 u
Change		- 42 u
After	25 u	63 u	63 u

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

42 u = 1302

1 u = 1302 ÷ 42 = 31

Amount that Raeann spent
= 63 u
= 63 x 31
= $1953 

Answer(s): (a) 25 : 105 : 63; (b) $1953