Three women, Olivia, Ivory and Anna went on a shopping spree. 70% of Olivia's spending was equal to ¹₆ of Ivory's spending. Anna's spending was  40% more than Ivory's. If Ivory spent another $1176, she would spend the same amount of money as Anna.

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

Olivia	Ivory	Anna
5x5	21x5
	5x21	7x21
25 u	105 u	147 u

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

710 of Olivia's spending = 16 of Ivory's spending
710 of Olivia's spending =1x76x7 of Ivory's spending
710 of Olivia's spending = 742 of Ivory's spending

Olivia : Ivory
10 : 42
5 : 21

Anna's spending in percent when compared to Ivory's
= 100% + 40%
= 140%

Ivory : Anna
100 : 140
5 : 7

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

Olivia : Ivory : Anna
25 : 105 : 147

(b)

	Olivia	Ivory	Anna
Before	25 u	105 u	147 u
Change		+ 42 u
After	25 u	147 u	147 u

Additional amount that Ivory would have to spend to be the same as Anna
= 147 u - 105 u
= 42 u

42 u = 1176

1 u = 1176 ÷ 42 = 28

Amount that Olivia spent
= 25 u
= 25 x 28
= $700 

Answer(s): (a) 25 : 105 : 147; (b) $700