Question Video: Adding and Subtracting Multidigit Numbers to Solve Word Problems | Nagwa Question Video: Adding and Subtracting Multidigit Numbers to Solve Word Problems | Nagwa

# Question Video: Adding and Subtracting Multidigit Numbers to Solve Word Problems Mathematics

Noah, Mason, and Benjamin decided to buy a new laptop for their father. The laptop costs \$1,750. Noah decided to pay \$650. Mason decided to pay \$500. How much should Benjamin pay so that they can buy the laptop?

05:13

### Video Transcript

Noah, Mason, and Benjamin decided to buy a new laptop for their father. The laptop costs 1,750 dollars. Noah decided to pay 650 dollars. Mason decided to pay 500 dollars. How much should Benjamin pay so that they can buy the laptop?

Here we’ve got what we call a word problem. It’s the sort of problem where we can’t see any symbols to tell us whether we need to add, subtract, multiply, or divide to help us solve it. Instead, we need to think carefully about the story behind the words, what do they describe. And there are a couple of things we can do to help ourselves here. A really useful tool for working out what we need to do to solve a problem is to draw a bar model. And in this question, we’ve been given a bar model already. Let’s re-read the question again right from the start, and we’ll look at how the bar model models it.

Our story begins with three brothers. We’ve got Noah, Mason, and Benjamin. And we’re told that they want to buy a new laptop for their father. The first really important piece of information we’re given is the cost of that laptop. It costs 1,750 dollars. Can you see this on the bar model? It’s written at the top here. And the way that our bar model’s been labeled, we can see that this represents the total amount. The whole length of the bar model represents 1,750 dollars. But how are our three brothers going to pay for this present for their father?

We’re told that Noah decided to pay 650 dollars. And we can see this labeled in the first part of our bar model. Next, we’re told that Mason decided to pay 500 dollars. And the second part of our bar model is labeled to show this amount. We’re finally asked how much should Benjamin pay. And we can see that this relates to the third part of our bar model. It’s the part that hasn’t been labeled, and it’s the part we need to find out.

So we’ve seen that the whole length of the bar model represents the whole cost of the laptop. And then its three parts represent the three parts of this whole amount that Noah, Mason, and Benjamin are going to pay. So what do we need to do to find the answer? As we’ve said already, there aren’t any symbols in the problem to tell us. But thankfully, we can use our bar model to help us. To find the amount that Benjamin needs to pay, we simply need to start with the whole amount and then subtract the two amounts that his brothers have already paid. Then we’ll know what’s left.

Now, there are two ways we could do this. One way to find the answer might be to start with the whole amount and subtract Noah’s payment and then whatever we’re left with to subtract Mason’s payment from it. Then we’d be left with the amount that Benjamin needs to pay. Or we could start with an addition. We could find out how much Noah and Mason have paid already. Then we’d need to subtract this from the whole amount. Now, it doesn’t matter which one of these two methods we use. Both of them are going to bring us to the right answer. Let’s use the first one, and then maybe we’ll show the second one just as a check.

So to begin with, we could subtract 650 from 1,750. This is the sort of calculation we could do in our heads because 650 is 100 less than 750. So we’ll be left with 1,100. And then if we take 1,100 and subtract the amount that Mason decides to pay, again, we could do this in our heads, 1,100 subtract 500. We know that if we had 1,000 and we subtracted 500, we’d have an answer of 500. So if we start off with 100 more than 1,000, but we still take away 500, our answer is going to be 100 more than 500. It looks like Benjamin’s going to need to pay 600 dollars, doesn’t it?

Let’s see whether that second method of ours would’ve found us the same answer. First, we’d need to add 650 and 500. This gives us a total of 1,150. This is the amount that those two brothers have paid altogether. And then if we subtract this from the whole amount, 1,750 take away 1,150, we’re left with 600.

We’ve used a bar model here to help us solve this two-step problem. And we’ve also talked about how we could solve it in two different ways. If a laptop costs 1,750 dollars, Noah pays 650 dollars of that, and Mason pays 500 dollars, then we know the amount that Benjamin needs to pay is 600 dollars.

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