Solve formula for a

Question

For altitudes up to 36,000 feet, the relationship between temperatures and altitude can be described by the formula t  = -0.0035a + g,  where t is the temperature in degrees Fahrenheit, a is the altitude in feet, and g is the ground temperature in degrees Fahrenheit.  Solve this formula for a

Answer 1

We need to isolate a in this equation.

 

Step 1:  Subtract g from both sides

 

t - g = -0.0035a + g-g

 

Step 2: We need to divide both sides by -0.0035 to get a to stand alone

 

(t-g)/(-0.0035) = a

 

A cleaner, more conventional  way of writing this is to get rid of the negative sign in the denominator.  In order to do this, we have to apply the negative sign to the variables in the numerator. We can do this by multiplying the numerator and denominator by -1

 

(-g)(-1) = g   (t)(-1) = -t

 

We can rearrange so it looks neater and the equation becomes  (g-t)/0.0035