Three women, Hilda, Emily and Zara went on a shopping spree. 70% of Hilda's spending was equal to ¹₆ of Emily's spending. Zara's spending was  40% less than Emily's. If Emily spent $4830 less, she would spend the same amount of money as Zara.

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

Hilda	Emily	Zara
5x5	21x5
	5x21	3x21
25 u	105 u	63 u

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

710 of Hilda's spending = 16 of Emily's spending
710 of Hilda's spending =1x76x7 of Emily's spending
710 of Hilda's spending = 742 of Emily's spending

Hilda : Emily
10 : 42
5 : 21

Zara's spending in percent when compared to Emily's
= 100% - 40%
= 60%

Emily : Zara
100 : 60
5 : 3

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

Hilda : Emily : Zara
25 : 105 : 63

(b)

	Hilda	Emily	Zara
Before	25 u	105 u	63 u
Change		- 42 u
After	25 u	63 u	63 u

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

42 u = 4830

1 u = 4830 ÷ 42 = 115

Amount that Zara spent
= 63 u
= 63 x 115
= $7245 

Answer(s): (a) 25 : 105 : 63; (b) $7245