How to Solve Word Problems in Math and Science

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If there’s one thing I know, it’s that most students struggle to solve word problems in math and science.

Have you ever looked at a word problem, especially on a test or exam, read it over 2 or 3 times, and then said “what?” out loud? It’s like reading absolute gibberish and expecting it to suddenly jump off the page and make sense.

The good news is, usually, it’s not the math that’s tricky, it’s figuring out how to pull the key information out of the problem. In other words, take the words and turn it into math.

You were probably taught the G.R.A.S.P. method in school. You know, Given, Required, Analysis, Solution, and Paraphrase. This is a great way to solve problems, but sometimes it’s not so easy to quickly identify what’s given and what’s required just from reading a word problem.

In this guide, I’m going to walk you through my step-by-step process for solving word problems in math or science.

Analyzing word problems in math or science courses

Watch the video or read the guide below.

1. Read through the problem

Let’s say we’re given the following problem in your grade 10 math course.

“The cost and revenue functions for a certain firm are given by C(x) = 12x + 20,000 and R(x) = 20x, respectively. Find the company’s profit function.”[1]

For a short problem like this, it’s simple enough to identify what’s happening, but if we had a question that was several sentences long we might find it more challenging. We’ll use this one as our example so we can see how the process works.

2. Highlight key information

Now that we’ve read through the problem, the next step is to highlight (or underline) all the key information. We’re looking for any given information and the required information (what the problem wants us to solve for).

“The cost and revenue functions for a certain firm are given by C(x) = 12x + 20,000 and R(x) = 20x, respectively. Find the company’s profit function.”[1]

We highlight the “cost” and “revenue” to show that they’re important. We’ll also highlight the corresponding functions “C(x) = 12x + 20,000” and “R(x) = 20x”. 

Last we highlight anything that tells us what we’re trying to solve for. In this case we want to “find” the “profit function”. 

3. Organize key information

Great, we’ve got all the relevant information – now let’s organize it.

This is where we use the first 2 steps of the G.R.A.S.P. process.

Given Information

  • Cost: C(x) = 12x + 20,000 
  • Revenue: R(x) = 20x

Required Information

  • Find the profit function, P(x).

4. Identify the method

Identifying the method is the Analysis part of the G.R.A.S.P. process. It’s also the part that requires some prerequisite math knowledge.

We know that Profit is Revenue minus Cost. P(x) = R(x) – C(x)

Our method will be to substitute our R(x) and P(x) functions from our Given Information into the P(x) equation we just wrote down.

5. Solve the problem

Once we’ve identified our given information, required information, and our analysis method we’ll solve the problem.

P(x) = 20x – (12x + 20,000)

P(x) = 20x – 12x – 20,000

P(x) = 8x – 20,000


References

  1. Tan, S. T. (2014). In Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach (10th ed., p. 41). Cengage Learning.

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