Question Video: Evaluating Variables in Given Linear Equations by Direct Substitution

Video Transcript

The equation 𝑡 equals eight ℎ shows the number of ice cream cones served by an ice cream truck in a number of hours. The variable ℎ represents the number of hours, and the variable 𝑡 represents the number of ice cream cones served. How many ice cream cones were served after two hours?

So the key thing here is our equation. And this equation shows the number of ice cream cones served by an ice cream truck in a number of hours. So we’ve got 𝑡 is equal to eight ℎ, where ℎ represents the number of hours and 𝑡 represents the number of ice cream cones.

What the question wants us to do is find out how many ice cream cones were served after two hours. So therefore, as ℎ is the number of hours, we can say that ℎ is gonna be equal to two. And what we need to do is substitute this into our equation. So therefore, 𝑡 is gonna be equal to eight multiplied by two. And that’s because eight ℎ means eight multiplied by ℎ. And if ℎ is equal to two, we’re gonna get 𝑡 is equal to 16 because, as we said, eight multiplied by two is 16. So therefore, we can say that 16 ice cream cones were served after two hours.

What we can do is just double-check this. And we can double-check it using an inverse operation. So what we can do is rearrange to find ℎ. So we’ve got 𝑡 equals eight ℎ. So therefore, we have a formula that tells us that 𝑡 divided by eight is equal to ℎ.

Well, to check it, what we can do is substitute in the value we found for 𝑡. And when we do that, we get 16 over eight is equal to ℎ. And we get ℎ is equal to two, which is great because 16 divided by eight is two. And two is what we started with because we want to know how many ice cream cones were served after two hours.

So we’ve checked our answer using inverse operations. And we can say yes, definitely, 16 cones were served after two hours.