# Formulas

A formula is an equation that contains at least two variables. Sometimes it is useful to solve a formula for one of the variables. That is, we write that variable in terms of the other variables.

Example 1

The density, d, of an object can be found by dividing its mass, m, by its volume, v.

That is,

Solve this formula for v.

 Solution d Multiply both sides of the equation by v, the denominator of the fraction. v Â· d Simplify. dv = m Divide both sides by d. v

Thus,

Note:

We could also solve for v by cross multiplying.

To check the solution, substitute for v in the original equation.

Example 2

The focal length, f, of a thin lens is related to p, the distance between the lens and the object, and q, the distance between the lens and the image, by the formula:

Solution

 Multiply each side by fpq, the LCD of the fractions. Cancel common factors. On the right side of the equation, factor out f. pqpq = fq + fp= f(q + p) Divide both sides by (q + p), the coefficient of f. = f
We leave the check to you.