How can real life problems involving one variable be modeled and solved?

Writing an equation to model a real-world problem is often easier when you take the information given in the problem and express it in verbal form by using a few key words. This is very similar to translating verbal phrases into variable expressions. The difference is you will be translating a verbal sentence into an equation. Then, you can solve the equation using inverse operations.

Let’s look at an example.

Monica purchased a pair of tennis shoes that had this sticker on the bottom of the shoe.

$99.00$65.99

Use a verbal model to write and solve an equation to determine the amount of money Monica saved by purchasing the shoes on sale.

First, write a verbal model to represent the problem.

Verbal Model:

Sales Price+Amount Saved=Original Price

Next, name the variable.

Let ‘

s

’ represent the amount saved.

Next, solve the equation you have written. Remember an equation is like a balance scale. To keep the scale balanced, what you do to one side of the equation you must also do to the other side. When solving an equation your goal is to isolate the variable on one side of the equation and the numerical terms on the other side. This is done by performing inverse operations.

65.99+s=99.00

First, isolate the variable ‘

s

’ by subtracting 65.99 from both sides of the equation. Subtraction is the inverse of addition.

65.99−65.99+s=99.00−65.99

Next, simplify each side.

s=33.01

The answer is $33.01.

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