# Video: Writing and Solving Linear Equations in a Real-World Context

Tim Burnham

The total time required to burn a single DVD is 18 minutes. Last weekend, Jason spent 90 minutes burning DVDs. Write a multiplication equation to determine the number of DVDs Jason burned, and then solve it.

02:10

### Video Transcript

The total time required to burn a single DVD is eighteen minutes. Last weekend, Jason spent ninety minutes burning DVDs. Write a multiplication equation to determine the number of DVDs that Jason burned, and then solve it.

First off, let’s define a variable. Let 𝑥 be the number of DVDs that Jason burned last weekend. So he burned 𝑥 DVDs, and each one of them took eighteen minutes to burn. And in total, he spent ninety minutes burning those DVDs. So we can say 𝑥 times eighteen, the number of DVDs times the number of minutes per DVD, equals ninety.

Now if we’re writing an algebraic equation, we wouldn’t normally leave that as 𝑥 times eighteen. We’d write it as eighteen 𝑥. Means the same thing, eighteen times 𝑥 or 𝑥 times eighteen, but it’s just a slightly more sophisticated algebra.

Well that’s the first part the question done then. We’ve written a multiplication equation to determine the number of DVDs, so now we’ve gotta go ahead and solve it. So eighteen times 𝑥 is equal to ninety. Well I want to know what 𝑥 is. Now the opposite of multiplying by eighteen is dividing by eighteen. So if I divide the left-hand side by eighteen, I’ve got 𝑥 times eighteen divided by eighteen. The eighteens are going to cancel, so I’m just gonna be left with 𝑥.

But the problem is I’ve just broken my equation; I’ve divided the left-hand side by eighteen but I didn’t divide the right-hand side by eighteen. So I need to do that; I need to divide the right-hand side by eighteen as well. Now, they’re equal. All we have to do now is divide ninety by eighteen or work out what do I need to multiply eighteen by to get ninety.

Well I know that five times ten is fifty and five times eight is forty, so five times eighteen is fifty plus forty; that’s ninety. So the answer is five. And answering the specific question how many DVDs did Jason burn, the answer was five.