The best way to start a word problem is to read the problem twice before writing anything down. Then you should decide what the unknowns are and assign variables to them (I personally prefer to assign x to the smaller of my unknowns. I find that this way I can stay consistent and always know what I am solving for). Most word problems consist of two main parts (which sometimes can be interchanged). The first part provides some information that can be used to set up the variables and the second part is used to relate the variables in an equation. If you can focus on these two parts of the problem the task of setting up the problem becomes considerably easier.

Example 1) The sum of three consecutive odd integers is 75. Find the numbers.

The two parts of this problem are: The numbers add up to 75, and the numbers are consecutive odd.

I’ll use the fact that they are consecutive odd ( for example 5,7 and 9) to set up the variables.

If we call the smallest of the three numbers x, the second number is going to be 2 bigger (because we have to skip an integer to get to the next odd integer) and by the same reasoning the third integer is going to be 2 bigger the second integer or 4 bigger the first. So we have:

First integer: x

Second integer: x + 2

Third integer: x + 4

Now we can use the second part of the problem that says they’ll add up to 75 to write an equation:

x + x + 2 + x + 4 = 75

Combine the like terms:

3x + 6 = 75

And solve by subtracting 6.

3x + 6 – 6 = 75 – 6

3x = 69

Divide both sides by 3

So x = 23. Then our numbers are: 23, 25 and 27.

Example 2) The length of a rectangle is 3 more than its width. Find the dimensions of the rectangle if the perimeter is 42 inches.

The two parts are: the length is 3 more than the width, and the perimeter is 42.

The unknowns are the width and the length. We’ll call the smaller one which is the width x.

Width: x

Length: x + 3

Now using the second part we’ll add two lengths and two widths to get the perimeter:

2x + 2(x + 3) = 42

2x + 2x + 6 = 42

4x + 6 = 42

4x +6 – 6 = 42 – 6

4x = 36 then divide both sides by 4

So we get x = 9. Then the dimensions of the rectangle are: 9 inches by 12 inches.

Example 3) Tracy is 5 years younger than John. In six years, the sum of their ages will be 37. Find their ages now.

The two parts are: the difference in their age, and the sum of their age.

The unknowns are their ages now. So, we will assign Tracy's age now the variable x.

Tracy's age now: x

John's age now: x + 5

The second part refers to the sum of their ages in 6 years. Before we can add their ages we need to increase each age by 6 since they both get older.

Tracy's age in 6 years: x + 6

John's age in 6 years: x + 11

(x + 6) + (x + 11) = 37

2x + 17 = 37

2x = 20

x = 10

So Tracy is 10 years old now and John is 15 years old now.