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David, Jennifer, and Matthew each have the same amount of money.
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David has only nickels, Jennifer has only dimes, and Matthew has only quarters.
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What is the least amount of money that each of them could have?
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This problem is asking us to think about ways to make the same amount of money, but using different coins.
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What information are we told to help us find the answer?
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Well, we’re told the three types of coins that each person has.
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David has only nickels and we know that one nickel has a value of five cents.
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Jennifer has only dimes and we know that one dime is worth 10 cents.
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And finally, Matthew has only quarters.
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We know that one whole dollar is worth 100 cents.
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So, a quarter dollar must be worth 25 cents.
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So we can see from this information, that the number of cents that David has must be a multiple of five.
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The number of cents that Jennifer has in total must be a multiple of 10.
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And Matthew’s total must be a multiple of 25.
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And the question also tells us that each of their amounts are the same.
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And we’re looking for the smallest possible answer.
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Let’s start by sketching a number line to see the possible amounts of money that Matthew could have.
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Matthew could have 25, 50, 75, or 100 cents, which is the same as a dollar because Matthew has only got quarters.
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You can’t make any other amounts.
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If we do the same for Jennifer, we’re going to need to count in multiples of 10.
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So Jennifer could have 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 cents.
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And we can see straightaway that Jennifer and Matthew could either have 50 cents or 100 cents.
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And then, they would both have the same amount.
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Now, the question asks us for the smallest possible answer.
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So let’s start with the smallest of those amounts and let’s check whether David could have 50 cents too.
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And remember David has a pile of nickels in front of him.
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And so we need to count in multiples of five.
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We know that 50 is a multiple of five.
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And it can be made out of nickels.
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It’s 10 nickels worth.
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And so the least amount of money that the children could have is 50 cents.