Video: Writing Algebraic Expressions in a Real-World Context

For a marathon, an athlete practiced on a track that is 𝑚 miles long. She ran for 5 laps each on Monday and on Wednesday and 4 laps on Friday. On Sunday, she ran for 18 miles. Write an expression in the simplest form that represents the total distance the athlete ran during her practice.

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Video Transcript

For a marathon, an athlete practiced on a track that is 𝑚 miles long. She ran for five laps each on Monday and on Wednesday and four laps on Friday. On Sunday, she ran for 18 miles. Write an expression in the simplest form that represents the total distance the athlete ran during her practice.

First of all, from a long worded question like this, we wanna work out what we’re actually looking for. And we can see that what we’re trying to look for is actually the total distance that the athlete ran. And we want to find this total distance in miles as these are the units that are mentioned within our question.

Okay, great! So let’s look at the information we have. We can see that the question tells us how many laps she ran on each day. So let’s write these down. So we got five laps on Monday and also five laps on Wednesday; be careful not to miss this one out because if you just looked at the numbers, you think it was five, four, and 18, but in fact there are two lots of five laps because it says that she ran for five laps each on Monday and on Wednesday. Then, she ran four laps on Friday. And then finally, on Sunday, she ran 18 miles.

Okay, great! So we’ve got all the information down. So what we can now do is just work out our total number of laps, which is gonna be five plus five plus four which is gonna give us 14 laps. Well, if we know that also we’ve got 14 laps, but each lap is worth 𝑚 miles, we can show that our total distance travelled in those 14 laps can be represented by 14 𝑚 because it’s 14 multiplied by 𝑚 miles.

Great! So we now know the total distance from Monday to Friday. Well, now that we know the total distance from Monday to Friday and we know the total distance for Sunday, we can solve the problem and actually write an expression in the simplest form. So we can say the total distance the athlete ran during her practice was 14𝑚 plus 18.

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