Introduction to Word Problems

In algebra word problems are commonplace, though they confuse many. Use this free lesson to help you learn how to solve word problems.

Problem 1 Answer

Here's Problem 1:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

Answer: $29

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

Step 1: Read through the problem carefully

The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it. Let's look at the problem again. The question is right there in plain sight:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

So is the information we'll need to answer the question:

Step 2: Represent the unknown numbers with variables

The unknown number in this problem is the cost of the family pass. We'll represent it with the variable f.

Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

In other words, we could say that the cost of a family pass equals half of $8, plus $25. To turn this into a problem we can solve, we'll have to translate it into math. Here's how:

  1. First, replace the cost of a family pass with our variable f.
  2. f equals half of $8 plus $25

  3. Next, take out the dollar signs and replace words like plus and equals with operators.
  4. f = half of 8 + 25

  5. Finally, translate the rest of the problem. Half of can be written as 1/2 times, or 1/2 ⋅ :
  6. f = 1/2 ⋅ 8 + 25

Step 4: Solve the problem

Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.

  1. f is already alone on the left side of the equation, so all we have to do is calculate the right side.
  2. f = 1/2 ⋅ 8 + 25

  3. First, multiply 1/2 by 8. 1/2 ⋅ 8 is 4.
  4. f = 4 + 25

  5. Next, add 4 and 25. 4 + 25 equals 29 .
  6. f = 29

That's it! f is equal to 29. In other words, the cost of a family pass is $29.

Step 5: Check your work

Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.

  1. We could translate this into this equation, with s standing for the cost of a single ticket.
  2. 1/2s = 29 - 25

  3. Let's work on the right side first. 29 - 25 is 4.
  4. 1/2s = 4

  5. To find the value of s, we have to get it alone on the left side of the equation. This means getting rid of 1/2. To do this, we'll multiply each side by the inverse of 1/2: 2.
  6. s = 8

According to our math, s = 8. In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

So now we're sure about the answer to our problem: The cost of a family pass is $29.