# Making Up a Formula to Solve Any Mathematical Problem

A formula is a rule which, in mathematical language, gives directions for finding the unknown value. Let’s see how such a rule works in a specific problem: If a worker earns \$4 an hour, how much money will he earn for several hours?

Since we do not know the total earnings, it should be indicated by x. From the wording of the problem and from your knowledge in arithmetic, you know that the total earnings are determined by multiplying the hourly rate of \$4 by the number of hours worked. This is the rule to be applied in this problem. How is this rule indicated mathematically? It is expressed by the formula x = 4 X t

In this formula the letter t stands for any number of hours. Whatever the number of hours, the total earnings will always  be 4 times (X) the number of hours. Two things are not known in this formula: the total earnings and the number of hours. The total earnings cannot be determined unless the number of hours is known.

The times sign can be omitted from the formula and the formula written as: x = 4t

This is a simple way of saying 4 times t. To take another example, 3 times one apple is 3 apples. The use of letters and numbers makes it possible to express multiplication without using the times sign. With two numbers, however, we cannot do this, because 2 X 3 is not the same as 23. Take away the times sign here and you have “twenty-three,” not “two times three.”

The given formula becomes useful when we apply it to specific problems. For example, if Ann earns \$4 an hour, how much will she earn in 5 hr (hours)? Apply the formula, but instead of t use the specific number 5. This procedure is called substitution. Thus, when we substitute 5 for t in this formula,x = 4twill be x = 4 X 5. This formula can serve to solve the problem. It has become an equation in which the left side is not known but the right side can be represented by a specific number. When we multiply 4 by 5, the right side of the equation becomes 20, or x = 20. This is the solution. Since Ann worked 5 hr at \$4 an hour, she earned \$20. Note that only numbers are used in the formula. Dollar signs (\$) and hours (hr) are not expressed.

In the above example, a formula made it possible to solve a problem based on the rule. You will have many opportunities to use formulas. People in technical jobs, such as electricians, machinists, or technical illustrators, use formulas regularly. Of course, scientists, engineers, and business executives also use formulas.

The formula discussed here is a very simple one, but some formulas are much more complicated. You will learn from this article how to work with simple formulas first, and, gradually, you will learn how to apply more involved formulas as we go along. Just keep on following me.

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