Video: Solving One-Variable Equations Embedded in a Real-Life Context

William drives the same distance to work, Monday through Friday. Last week, he drove 30 miles over the weekend, for a total of 165 miles throughout the week. Solve 5𝑥 + 30 = 165 for 𝑥 to determine the distance William drives every day to work.

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Video Transcript

William drives the same distance to work Monday through Friday. Last week, he drove 30 miles over the weekend, for a total of 165 miles throughout the week. Solve five 𝑥 plus 30 equals 165 for 𝑥 to determine the distance William drives every day to work.

So in this question, an equation has been formed for a real-life context. So let’s think how did this equation get formed. Well, we’ve already been told that 𝑥 is the distance per day. So we’ve got 𝑥 in our equation. And then we’re told that William drives the same distance to work Monday through Friday. So we’ve got Monday, Tuesday, Wednesday, Thursday, Friday. So that’s five days. So therefore, from our equation, we can say that five is the number of days driven to work and 𝑥 is the distance per day. Then we were also told that 30 miles is the distance he traveled over the weekend. And then, finally, 165 miles is the total distance for the week.

Okay, great, so we’ve seen now how we formed our equation. And that’s because if we multiply the number of days driven to work by the total distance per day and then add on the weekend distance, that will give us the total distance for the week. So now what we need to do is to solve this equation to find 𝑥.

Well, the first thing we need to do to solve this equation is subtract 30 from each side. And that’s because we want our 𝑥 left on its own on the left-hand side. And when we do that, we get five 𝑥 is equal to 135. That’s because if you’ve got five 𝑥 plus 30 and we subtract 30, it just leaves us with five 𝑥. And then 165 minus 30 is 135.

And then the next step is to divide both sides of the equation by five. And that’s cause we want a single 𝑥. So five 𝑥 divided by five is 𝑥. And 135 divided by five is 27. And we can work that out using short division or the bus stop method. And the way we’d do this is we’d see, first of all, how many fives go into one, which is zero. And then we carry the one. So then how many fives go into 13, which is two remainder three. Then how many fives go into 35, cause we carry that three. Well, it’s a seven so that the answer is 27. So therefore, we can say that William travels 27 miles to work each day.

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