Question Video: Making the Same Amount of Money with Different Coins

David, Jennifer, and Matthew each have the same amount of money. David has only nickels, Jennifer has only dimes, and Matthew has only quarters. What is the least amount of money that each of them could have?

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Video Transcript

David, Jennifer, and Matthew each have the same amount of money. David has only nickels, Jennifer has only dimes, and Matthew has only quarters. What is the least amount of money that each of them could have?

This problem is asking us to think about ways to make the same amount of money, but using different coins. What information are we told to help us find the answer? Well, we’re told the three types of coins that each person has. David has only nickels and we know that one nickel has a value of five cents. Jennifer has only dimes and we know that one dime is worth 10 cents. And finally, Matthew has only quarters. We know that one whole dollar is worth 100 cents. So, a quarter dollar must be worth 25 cents.

So we can see from this information, that the number of cents that David has must be a multiple of five. The number of cents that Jennifer has in total must be a multiple of 10. And Matthew’s total must be a multiple of 25. And the question also tells us that each of their amounts are the same. And we’re looking for the smallest possible answer.

Let’s start by sketching a number line to see the possible amounts of money that Matthew could have. Matthew could have 25, 50, 75, or 100 cents, which is the same as a dollar because Matthew has only got quarters. You can’t make any other amounts.

If we do the same for Jennifer, we’re going to need to count in multiples of 10. So Jennifer could have 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 cents. And we can see straightaway that Jennifer and Matthew could either have 50 cents or 100 cents. And then, they would both have the same amount.

Now, the question asks us for the smallest possible answer. So let’s start with the smallest of those amounts and let’s check whether David could have 50 cents too. And remember David has a pile of nickels in front of him. And so we need to count in multiples of five. We know that 50 is a multiple of five. And it can be made out of nickels. It’s 10 nickels worth.

And so the least amount of money that the children could have is 50 cents.

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