Three women, Gillian, Ivory and Irene went on a shopping spree. 70% of Gillian's spending was equal to ¹₆ of Ivory's spending. Irene's spending was  40% more than Ivory's. If Ivory spent another $3486, she would spend the same amount of money as Irene.

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

Gillian	Ivory	Irene
5x5	21x5
	5x21	7x21
25 u	105 u	147 u

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

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

Gillian : Ivory
10 : 42
5 : 21

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

Ivory : Irene
100 : 140
5 : 7

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

Gillian : Ivory : Irene
25 : 105 : 147

(b)

	Gillian	Ivory	Irene
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 Irene
= 147 u - 105 u
= 42 u

42 u = 3486

1 u = 3486 ÷ 42 = 83

Amount that Gillian spent
= 25 u
= 25 x 83
= $2075 

Answer(s): (a) 25 : 105 : 147; (b) $2075