So far, you’ve encountered verbal representations that include pretty obvious keywords indicating mathematical operators. Sometimes, though, the language in a word problem is not obvious. You may have to figure out what a problem is saying by analyzing all of the key information provided in the problem. You may also have to draw on your past experiences in math to figure out what to do.
Read the problem scenario below. Notice how it doesn’t have any of the normal keywords for mathematical operators in it.
A movie theater spends $4000 for a copy of a film and the rights to show the movie. The theater charges $8.50 for each adult ticket. If the movie theater wants to make $5000 in profit, how many tickets do they need to sell?
Although the language in this problem scenario doesn’t include any of the keywords that are typically used for mathematical operators, it deals with costs and profits in a way that is very similar to the previous problem. You can still construct an algebraic equation if you know what questions to ask yourself.
Study the tabs below, then click each one to see how this is done.
Take note of any key information, such as numbers and what they represent, so you can define what you know in the problem.
A movie theater spends $4000 for a copy of a film the rights to show the movie. The theater charges $8.50 for each adult ticket. If the movie theater wants to make $5000 in profit, how many tickets do they need to sell?
What do you know already, based on the words in this problem?
- cost to screen a movie = $4000
- charge per ticket = $8.50
- profit wanted = $5000
Locate the question in the scenario and determine what it asks for. This is the unknown in the problem and therefore will be defined by a variable.
A movie theater spends $4000 for a copy of a film and the rights to show the movie. The theater charges $8.50 for each adult ticket. If the movie theater wants to make $5000 in profit, how many tickets do they need to sell?
What is the unknown in this problem?
the number of tickets, or t
The verbal representation of this scenario does not include the word equals or similar. Therefore, you have to figure out that what the movie theater earns through sales must equal the sum of the cost and profit.
What equals what? How can you write this part of the word problem as an equation rather than an expression?
the amount charged per ticket · the number of tickets = the cost to screen the movie + the profit wanted
You already know that the charge per ticket times the number of tickets equals the sum of the cost to screen the movie plus the profit the theater wants to make. Your last step is to translate that information into an equation using only numbers, variables, and operators.
What equation represents the situation?
\(\mathsf{ $8.50t = $4000 + $5000 }\)
Let's Practice
Try using this process on your own, based on the problem scenario below.
A pet food company wants to sell bags of rabbit food. It costs the company $15,000 to produce the food, and they hope to break even after selling 4000 bags. What amount of money must they charge per bag to avoid spending more than they make?
Translate the scenario above into an equation, using the questions below to guide you through the process. Once you know the answer to each question, click the question to check your work.
The cost of production is $15,000, and the company wants to make a profit after selling 4000 bags of food. |
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You do not know what price the company should charge for the bags of rabbit food. |
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The pet food company wants to break even after selling 4000 bags of food. In other words, they want the product of the cost per bag times the number of bags sold to equal the cost of production. |
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Since the product of the cost per bag times the number of bags sold must equal the cost of production, you can write this equation to represent the situation. |
