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

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.

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:

- A single ticket costs
**$8**. - The family pass costs
**$25 more**than**half**the price of the single ticket.

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

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:

- First, replace
**the cost of a family pass**with our variable*f*. - Next, take out the dollar signs and replace words like
**plus**and**equals**with operators. - Finally, translate the rest of the problem.
**Half of**can be written as 1/2 times, or 1/2 ⋅ :

f equals half of $8 plus $25

f = half of 8 + 25

f = 1/2 ⋅ 8 + 25

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.

*f*is already alone on the left side of the equation, so all we have to do is calculate the right side.- First, multiply 1/2 by 8.
**1/2 ⋅ 8**is 4. - Next, add 4 and 25.
**4 + 25**equals 29 .

f = 1/2 ⋅ 8 + 25

f = 4 + 25

f = 29

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

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.

- We could translate this into this equation, with
*s*standing for the cost of a single ticket. - Let's work on the right side first.
**29 - 25**is 4. - 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.

1/2s = 29 - 25

1/2s = 4

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.