Three women, Hilda, Olivia and Gabby went on a shopping spree. 70% of Hilda's spending was equal to ¹₂ of Olivia's spending. Gabby's spending was  50% more than Olivia's. If Olivia spent another $539, she would spend the same amount of money as Gabby.

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

Hilda	Olivia	Gabby
5x2	7x2
	2x7	3x7
10 u	14 u	21 u

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

710 of Hilda's spending = 12 of Olivia's spending
710 of Hilda's spending =1x72x7 of Olivia's spending
710 of Hilda's spending = 714 of Olivia's spending

Hilda : Olivia
10 : 14
5 : 7

Gabby's spending in percent when compared to Olivia's
= 100% + 50%
= 150%

Olivia : Gabby
100 : 150
2 : 3

Olivia's spending is the repeated identity.  Make Olivia's spending the same.  LCM of 7 and 2 is 14.

Hilda : Olivia : Gabby
10 : 14 : 21

(b)

	Hilda	Olivia	Gabby
Before	10 u	14 u	21 u
Change		+ 7 u
After	10 u	21 u	21 u

Additional amount that Olivia would have to spend to be the same as Gabby
= 21 u - 14 u
= 7 u

7 u = 539

1 u = 539 ÷ 7 = 77

Amount that Hilda spent
= 10 u
= 10 x 77
= $770 

Answer(s): (a) 10 : 14 : 21; (b) $770