Here are some examples solving number problems.

##### Example 1

When 6 times a number is increased by 4, the result is 40. Find the number.

First, circle what you must find— *the number.* Letting *x* stand for the number gives the equation

6 *x* + 4 = 40

Subtracting 4 from each side gives

6 *x* = 36

Dividing by 6 gives

*x* = 6

So the number is 6.

##### Example 2

One number exceeds another number by 5. If the sum of the two numbers is 39, find the smaller number.

First, circle what you are looking for— *the smaller number.* Now, let the smaller number equal *x.* Therefore, the larger number equals *x* + 5. Now, use the problem to set up an equation.

Therefore, the smaller number is 17.

##### Example 3

If one number is three times as large as another number and the smaller number is increased by 19, the result is 6 less than twice the larger number. What is the larger number?

First, circle what you must find— *the larger number.* Let the smaller number equal *x*. Therefore, the larger number will be 3 *x*. Now, using the problem, set up an equation.

Therefore, the larger number, 3 *x*, is 3(5), or 15.

##### Example 4

The sum of three consecutive integers is 306. What is the largest integer?

First, circle what you must find— *the largest integer.* Let the smallest integer equal *x*; let *x* + 1 equal the next integer; let the largest integer equal *x* + 2. Now, use the problem to set up an equation.

Therefore, the largest integer, *x* + 2 = 101 + 2 = 103.