Three women, Sarah, Ivory and Zara went on a shopping spree. 70% of Sarah's spending was equal to ¹₂ of Ivory's spending. Zara's spending was  60% more than Ivory's. If Ivory spent another $756, she would spend the same amount of money as Zara.

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

Sarah	Ivory	Zara
5x5	7x5
	5x7	8x7
25 u	35 u	56 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Sarah's spending is equal to ¹₂ of Ivory's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Sarah's spending = 12 of Ivory's spending
710 of Sarah's spending =1x72x7 of Ivory's spending
710 of Sarah's spending = 714 of Ivory's spending

Sarah : Ivory
10 : 14
5 : 7

Zara's spending in percent when compared to Ivory's
= 100% + 60%
= 160%

Ivory : Zara
100 : 160
5 : 8

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

Sarah : Ivory : Zara
25 : 35 : 56

(b)

	Sarah	Ivory	Zara
Before	25 u	35 u	56 u
Change		+ 21 u
After	25 u	56 u	56 u

Additional amount that Ivory would have to spend to be the same as Zara
= 56 u - 35 u
= 21 u

21 u = 756

1 u = 756 ÷ 21 = 36

Amount that Sarah spent
= 25 u
= 25 x 36
= $900 

Answer(s): (a) 25 : 35 : 56; (b) $900