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changing application problems into equations

the distance to Georgia is 1/2 the distance to Tennessee.

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Michael K. | Math Major Michael works as Engineer and tutors in MathMath Major Michael works as Engineer and...
4.9 4.9 (37 lesson ratings) (37)
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There are keywords that can be replaced by mathematical expressions without exception. Let me rewrite the phrase. "the distance to Georgia (Dg) is (=) 1/2 of (*) the distance to Tennessee (Dt)." I am using the variable Dg to be the distance to Georgia and Dt to be the distance to Tennessee. The equation is Dg = 1/2*Dt. 

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)
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Given:     The distance to Georgia is 1/2 the distance to Tennessee

First assign variables to the given parameters...let 'x' represent the distance to Georgia and 'y' represent the distance to Tennessee. That is,

          x = distance to Georgia 

          y = distance to Tennessee

Since we are given that the distance to Georgia (x) is 1/2 the distance to Tennessee (y), then the distance to Georgia is given by the following equation: 

          x = (1/2)y         

Notice that multiplying both sides of the equation above by 2 generates an equation that defines the distance to Tennessee (y) in terms of the distance to Georgia (x):

          2•x = 2•(1/2)y

           2x = (2/2)y

           2x = (1)y

            y = 2x