Using units to solve problems: Toy factory | Working with units | Algebra I | Khan Academy

We're told a factory makes toys that are sold for ten dollars a piece. The factory has 40 workers, and they each produce 25 toys a day. The factory is open five days a week. What is the total value of toys the factory produces in a day?

Pause this video and see if you can figure that out.

All right, so let's just think about a day. Before I even look at this information, if I could figure out the value per toy and then multiply that times the number of toys produced in a day, then we would have the total value.

Let’s still see if they give us that information. Well, the value per toy, they say the toys are sold for 10 a piece. So we could write this this way: 10 per toy.

And then they do tell us, or they give us the information that we need to figure out how many are produced in a day. We have 40 workers, and they each produce 25 toys a day.

So the amount that's produced in a day is going to be 40 workers times 25 toys per worker. Now I could say 25 toys per worker per day, and that makes the units a little complicated.

Or I could just realize that this entire expression I'm creating is talking about one day. So the total number of toys produced in a day is going to be the product of these things, and we can see that the units work out.

Just to make sure that we're getting in the right direction, a toy in the denominator cancels out with the toys in the numerator. Workers, when you multiply, this would be in the numerator; thus, this in the denominator.

So workers, workers cancel out, and so I'm going to be left with 10 times 40 times 25 dollars. I do want it written in dollars, and so this is going to be equal to 10 times 40, which is 400.

And then 400 times 25, let's see, that's going to be 4 times 25 times 100. So that's 100 times 100, which is 10,000, and then the units we're left with is dollars.

Now you might be saying, "Wait, we didn't use all of the information," and that's true; we didn't use the fact that the factory is open five days a week.

We didn't need to use that information; that would have been useful if they said, "What is the total value of toys the factory produces in a week?" Then we would have said their value per day is ten thousand dollars, and we could even write it this way: per day, and then multiply that times five days in a week.

That would have given us the total value of the production in a week, but that's not what they're asking for. So we don't need that other information, and so we don't have to go to that step.

This was really just extra information, probably to distract you a bit.