Video: Solving Multi-step Problems Using Multiplication and Addition

On a given day at a restaurant, 39 people ordered the shrimp plate for $15.50 and French fries for $4.50. Determine how much money the restaurant earned that day.

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Video Transcript

On a given day at a restaurant, 39 people ordered the shrimp plate for 15 dollars 50 and French fries for four dollars 50. Determine how much money the restaurant earned that day.

Our problem describes a day at a restaurant. This is a day where 39 people order two different things from the menu. They order the shrimp plate, which costs 15 dollars 50. And they also order French fries, which cost four dollars 50. And we’re asked to determine or find out how much money the restaurant earned that day. This problem involves more than one step. And there are two ways to find the answer. We could sketch an area model of multiplication to understand how we could find the answer.

There are 39 people at the restaurant. And one of the things we know they ordered is the shrimp plate for 15 dollars 50. And so, to calculate the amount of money that they spend on shrimps altogether, we need to work out 39 multiplied by 15.5, which represents 15 dollars 50. And of course, they also buy French fries, which cost four dollars 50. And again, we need to find 39 lots of French fries. So we calculate 39 multiplied by 4.5. So here, we have two multiplications that we need to work out. And they both involve multiplying 39 by a decimal. After we’ve worked out these multiplications, we need to add them together to find the overall total.

Now, this is one way that we could use to find the answer. And perhaps, if the numbers were different, it might be quite a good way to find the answer. But given the numbers that we’ve got, there’s a much quicker method we could use. What if we added together 15 dollars 50 and four dollars 50 before we started? How could this help us? Well, firstly, we’d only need to work out one multiplication to find the answer. But secondly, and more importantly, if we look closely at these numbers, if we add them together, they’re going to make a whole number. 15 dollars plus four dollars gives us 19 dollars. And if we add the two lots of 50 cents on the end, we have one more dollar. So 15 dollars 50 plus four dollars 50 equals 20 dollars.

Each of the 39 people at the restaurant spent 20 dollars on food. Now, we can see why this is such a quick method. All we have to do to find the answer is to multiply 39 by 20. Now, we know 20 is double 10. Why don’t we multiply 39 by 10 and then double the answer? When we multiply any number by 10, its digits shift one place to the left. And so, 39 is going to become 390. Now, we can double 390 to find out what 39 lots of 20 is. Zero plus zero equals zero. Nine tens plus nine tens equals 18 tens, which is the same as 108 tens. And finally, 300 plus 300 plus the one we’ve exchanged equals 700.

We found the answer without having to multiply any decimals at all. We notice that if we added together the two prices, it came to 20 dollars. And so, to find the total amount of money that the restaurant earned, all we had to do was to multiply 20 dollars by the 39 people that they were in the restaurant.

So if there were 39 people at the restaurant and they ordered the shrimp plate for 15 dollars 50 and French fries for four dollars 50, the amount of money that the restaurant earned is 780 dollars.

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