Three women, Diana, Emily and Eva went on a shopping spree. 70% of Diana's spending was equal to ¹₅ of Emily's spending. Eva's spending was  70% less than Emily's. If Emily spent $4851 less, she would spend the same amount of money as Eva.

1. Find the ratio of Diana's spending to Emily's to Eva's.
2. How much did Eva spend?

Diana	Emily	Eva
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

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

710 of Diana's spending = 15 of Emily's spending
710 of Diana's spending =1x75x7 of Emily's spending
710 of Diana's spending = 735 of Emily's spending

Diana : Emily
10 : 35
2 : 7

Eva's spending in percent when compared to Emily's
= 100% - 70%
= 30%

Emily : Eva
100 : 30
10 : 3

Emily's spending is the repeated identity.  Make Emily's spending the same.  LCM of 7 and 10 is 70.

Diana : Emily : Eva
20 : 70 : 21

(b)

	Diana	Emily	Eva
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

Additional amount that Emily would have to spend less to be the same as Eva
= 70 u - 21 u
= 49 u

49 u = 4851

1 u = 4851 ÷ 49 = 99

Amount that Eva spent
= 21 u
= 21 x 99
= $2079 

Answer(s): (a) 20 : 70 : 21; (b) $2079