Skill: Represent problems with equations

To represent a problem with an equation:

1. Find the unknown quantity. Choose a letter, such as $g$, to stand for it.
2. List the known quantities.
3. Notice the relationship between the quantities. Look for words such as total, each, left, more, or equal groups.
4. Write an equation with an equality sign, $=$. Make sure both sides describe the same amount.
5. Check the units and meaning of your equation.

Example

A class has $28$ students. Then $4$ more students join. The class is divided equally into $4$ groups. How many students are in each group?

Step 1: Choose a variable.

Let $g$ represent the number of students in each group.

Step 2: Combine the students.

The class has $28+4$ students altogether.

Step 3: Represent dividing equally.

Dividing the total number of students into $4$ equal groups gives

$$g=\frac{28+4}{4}.$$

This is an equation because it has a variable, numbers, operations, and an equality sign.

Step 4: Check the equation.

First calculate inside the parentheses:

$$g=\frac{32}{4}=8.$$

There are $8$ students in each group. The units make sense because $g$ represents students, and the equation uses the total number of students divided by the number of groups.