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

## changing application problems into equations

# 2 Answers

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**