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## changing application problems into equations

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

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.

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