Three women, Esther, Hilda and Emily went on a shopping spree. 30% of Esther's spending was equal to ¹₆ of Hilda's spending. Emily's spending was  25% more than Hilda's. If Hilda spent another $477, she would spend the same amount of money as Emily.

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

Esther	Hilda	Emily
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

310 of Esther's spending = 16 of Hilda's spending
310 of Esther's spending =1x36x3 of Hilda's spending
310 of Esther's spending = 318 of Hilda's spending

Esther : Hilda
10 : 18
5 : 9

Emily's spending in percent when compared to Hilda's
= 100% + 25%
= 125%

Hilda : Emily
100 : 125
4 : 5

Hilda's spending is the repeated identity.  Make Hilda's spending the same.  LCM of 9 and 4 is 36.

Esther : Hilda : Emily
20 : 36 : 45

(b)

	Esther	Hilda	Emily
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

Additional amount that Hilda would have to spend to be the same as Emily
= 45 u - 36 u
= 9 u

9 u = 477

1 u = 477 ÷ 9 = 53

Amount that Esther spent
= 20 u
= 20 x 53
= $1060 

Answer(s): (a) 20 : 36 : 45; (b) $1060