2 step estimation word problems

We are told that a race car driver has 28 cars. Each car has four tires. He has to replace all the tires on the cars. He has 22 tires right now. Estimate the total number of tires he needs to buy. So pause this video and see if you can do that. And the key word here is estimate. You don't have to figure out exactly; you just need to figure out roughly the total number of tires he needs to buy.

All right, now let's work through this together. And as I mentioned, the key word here is estimate. Estimating is something we'll do throughout our lives. I probably do it once a day at least. And when you're estimating, you want to make all the numbers roughly right but also think about, hey, what do I need to—how do I need to think about them in order to make the computation a little bit easier or a little bit friendlier?

So if I wanted to figure out exactly how many tires he needed to buy, I would say, hey, he has 28 cars. He has 28 cars, and each car has four tires. So each car has four tires. So if you wanted to know the total number of tires, you would multiply 28 times 4. And then it says he has to replace all the tires on the cars. If he didn't have any, this is the number that he would have to replace. But it says he has 22 tires right now.

So if we were trying to figure out exactly, you would say 28 times 4. That's how many he needs to replace. But he already has 22, so you subtract that out. And then this whole number would be the number he needs to buy. Now this calculation isn't so easy to do, especially if you're doing it on a napkin or in your head. But that's why we're going to estimate.

So for estimating, we say, hey, what's a friendlier number than 28? Well, 28 is pretty close to 30. So I could say, so if I say, hey, 28 is pretty close to 30. So that's our way of making the 28 a little bit friendlier. 4 is already pretty easy to deal with. And then the 22, well, that could be a lot easier to deal with if instead of it being a 22, if that were, let's say, that's approximately equal to 20.

So 22 is approximately—roughly equal—that's what these squiggly equal signs mean: 20. And so that simplifies the calculation a lot. We could say that this thing up here is roughly equal to he roughly has 30 cars, and each of those cars need four tires. And then he's going to figure out the total number of tires he needs to replace. But then he subtracts out the number that he already has. So instead of subtracting out 22, we're going to subtract out roughly how many he already has—roughly 20.

And this computation right here is a lot easier to do in our head. 3 times 4 is 12, so 30 times 4 is 120. So this part right over here is 120, and then you subtract 20 from that. Well, 120 minus 20—well, that is going to be 100. So he roughly needs, if I were to estimate, the total number of tires he needs to buy, it would be about 100 tires.