Three women, Emma, Gabby and Kylie went on a shopping spree. 70% of Emma's spending was equal to ¹₂ of Gabby's spending. Kylie's spending was  25% more than Gabby's. If Gabby spent another $623, she would spend the same amount of money as Kylie.

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

Emma	Gabby	Kylie
5x4	7x4
	4x7	5x7
20 u	28 u	35 u

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

710 of Emma's spending = 12 of Gabby's spending
710 of Emma's spending =1x72x7 of Gabby's spending
710 of Emma's spending = 714 of Gabby's spending

Emma : Gabby
10 : 14
5 : 7

Kylie's spending in percent when compared to Gabby's
= 100% + 25%
= 125%

Gabby : Kylie
100 : 125
4 : 5

Gabby's spending is the repeated identity.  Make Gabby's spending the same.  LCM of 7 and 4 is 28.

Emma : Gabby : Kylie
20 : 28 : 35

(b)

	Emma	Gabby	Kylie
Before	20 u	28 u	35 u
Change		+ 7 u
After	20 u	35 u	35 u

Additional amount that Gabby would have to spend to be the same as Kylie
= 35 u - 28 u
= 7 u

7 u = 623

1 u = 623 ÷ 7 = 89

Amount that Emma spent
= 20 u
= 20 x 89
= $1780 

Answer(s): (a) 20 : 28 : 35; (b) $1780