Length word problem example

We're told that Pilar has 85 inches of ribbon. She gives her friend Nico 19 inches of ribbon. How much ribbon does Pilar have left? Pause this video and see if you can figure that out.

All right, now let's do it together. So Pilar is starting with 85 inches of ribbon, and I could represent that with what's sometimes known as a tape diagram. I guess we could call it a ribbon diagram in this case.

So let's say the width of this rectangle, or this tape, or this ribbon represents the length of Pilar's ribbon. So this is 85 inches of ribbon right over here. She gives her friend Nico 19 inches of the ribbon. I'll do that in red, so she gives away 19 inches.

So I could think about giving away 19 inches, and this is just, I'm not doing it exactly, but you get a sense of things. So 19 inches might be about that much. So that's 19 inches that Pilar gives away.

So how much ribbon does Pilar have left? Well, it would be this section right over here. Now, how do we figure out how much she has left, this question mark right over here?

Well, there's a couple of ways to think about it. You could say 19 plus the question mark is equal to 85. Let me write that down. 19 plus question mark plus what we're trying to figure out is equal to 85.

So the amount she gave away plus the amount she has left is equal to 85. Or you could say, if I start with 85 and if I were to take away 19, well, that's what I have left.

So you could also say that question mark, the amount that she has left, is equal to 85 minus 19. So what is 85 minus 19? Well, there's a bunch of ways that we can compute it.

One way to do it is I could rewrite 85 as 80 plus 5, essentially separate the tens place from the ones place. We have eight tens, which is the same thing as 80, and then five ones, and then rewrite 19 as 10 and 9.

So if I'm subtracting 19, I'm really subtracting 10 and subtracting 9. Now why is that useful? Well, it's pretty straightforward to say that, all right, 80 minus 10 is going to be equal to 70. Eight tens minus one ten is going to be equal to seven tens.

And so I could rewrite this as 70 plus 5 minus 9. Now, if I just try to figure out what 5 minus 9 is, we get into a little bit of trouble because 9 is bigger than 5.

But what if we were to rewrite 9 in two parts? If we were to say, look, 9 is the same thing as 4 plus 5. So if I'm subtracting 9, that's the same thing as subtracting 5 and then subtracting 4.

And this makes it a little bit easier because we know what that 5 minus 5 is: 0. And so we can rewrite this as 70 minus 4. Now what's that going to be?

Well, we know that 10 minus 4 is equal to 6, so 70 minus 4 is going to be equal to 66. And we're all done. That's how much ribbon she has: 66 inches of ribbon left.