Three women, Hilda, Tina and Eva went on a shopping spree. 30% of Hilda's spending was equal to ¹₂ of Tina's spending. Eva's spending was  70% less than Tina's. If Tina spent $2457 less, she would spend the same amount of money as Eva.

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

Hilda	Tina	Eva
5x10	3x10
	10x3	3x3
50 u	30 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Hilda's spending is equal to ¹₂ of Tina's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Hilda's spending = 12 of Tina's spending
310 of Hilda's spending =1x32x3 of Tina's spending
310 of Hilda's spending = 36 of Tina's spending

Hilda : Tina
10 : 6
5 : 3

Eva's spending in percent when compared to Tina's
= 100% - 70%
= 30%

Tina : Eva
100 : 30
10 : 3

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 3 and 10 is 30.

Hilda : Tina : Eva
50 : 30 : 9

(b)

	Hilda	Tina	Eva
Before	50 u	30 u	9 u
Change		- 21 u
After	50 u	9 u	9 u

Additional amount that Tina would have to spend less to be the same as Eva
= 30 u - 9 u
= 21 u

21 u = 2457

1 u = 2457 ÷ 21 = 117

Amount that Eva spent
= 9 u
= 9 x 117
= $1053 

Answer(s): (a) 50 : 30 : 9; (b) $1053