In this chapter, you became familiar with some formulas used in geometry. Formulas are also very useful in the sciences and social sciences—fields such as chemistry, physics, biology, psychology, sociology, and criminal justice. Healthcare workers use formulas, too, even for something as routine as dispensing medicine. The widely used spreadsheet program Microsoft Excel^TM relies on formulas to do its calculations. Many teachers use spreadsheets to apply formulas to compute student grades. It is important to be familiar with formulas and be able to manipulate them easily.

In some examples, we used the formula [latex]d=rt[/latex]. This formula gives the value of [latex]d[/latex] when you substitute in the values of [latex]r[/latex] and [latex]t[/latex]. But in another example, we had to find the value of [latex]t[/latex]. We substituted in values of [latex]d[/latex] and [latex]r[/latex] and then used algebra to solve for [latex]t[/latex]. If you had to do this often, you might wonder why there isn’t a formula that gives the value of [latex]t[/latex] when you substitute in the values of [latex]d[/latex] and [latex]r[/latex]. We can get a formula like this by solving the formula [latex]d=rt[/latex] for [latex]t[/latex].

Let’s try a few examples, starting with the distance, rate, and time formula we used above.

We say the formula [latex]t={\Large\frac{d}{r}}[/latex] is solved for [latex]t[/latex]. We can use this version of the formula any time we are given the distance and rate and need to find the time.

We used the formula [latex]A=\Large\frac{1}{2}\normalsize bh[/latex] to find the area of a triangle when we were given the base and height. In the next example, we will solve this formula for the height.

Previously, we used the formula [latex]I=Prt[/latex] to calculate simple interest, where [latex]I[/latex] is interest, [latex]P[/latex] is principal, [latex]r[/latex] is rate as a decimal, and [latex]t[/latex] is time in years.

Watch the following video to see another example of how to solve an equation for a specific variable.

Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually [latex]x[/latex] and [latex]y[/latex]. You might be given an equation that is solved for [latex]y[/latex] and you need to solve it for [latex]x[/latex], or vice versa. In the following example, we’re given an equation with both [latex]x[/latex] and [latex]y[/latex] on the same side and we’ll solve it for [latex]y[/latex]. To do this, we will follow the same steps that we used to solve a formula for a specific variable.

In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide?

In the following video we show another example of how to solve an equation for a specific variable.