Three women, Gillian, Jean and Hazel went on a shopping spree. 30% of Gillian's spending was equal to ¹₆ of Jean's spending. Hazel's spending was  60% more than Jean's. If Jean spent another $621, she would spend the same amount of money as Hazel.

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

Gillian	Jean	Hazel
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Gillian's spending is equal to ¹₆ of Jean's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Gillian's spending = 16 of Jean's spending
310 of Gillian's spending =1x36x3 of Jean's spending
310 of Gillian's spending = 318 of Jean's spending

Gillian : Jean
10 : 18
5 : 9

Hazel's spending in percent when compared to Jean's
= 100% + 60%
= 160%

Jean : Hazel
100 : 160
5 : 8

Jean's spending is the repeated identity.  Make Jean's spending the same.  LCM of 9 and 5 is 45.

Gillian : Jean : Hazel
25 : 45 : 72

(b)

	Gillian	Jean	Hazel
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Jean would have to spend to be the same as Hazel
= 72 u - 45 u
= 27 u

27 u = 621

1 u = 621 ÷ 27 = 23

Amount that Gillian spent
= 25 u
= 25 x 23
= $575 

Answer(s): (a) 25 : 45 : 72; (b) $575