WEBVTT

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Here is the problem: The sum of three consecutive integers is 72. What is the smallest?

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3 consecutive integers with sum 72. 3 consecutive integers with sum 72.

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Read the problem. 3 consecutive integers with sum 72.

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Name the integers. Call the smallest one x. Consecutive integers differ by 1, so the 3 numbers are x, (x plus 1), (x plus 2).

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Write the equation. x plus (x plus 1) plus (x plus 2) equals 72.

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Combine like terms. There are 3 copies of x, and the constants add to 1 times (0 plus 1 plus … plus 2) equals 3. So 3x plus 3 equals 72.

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Solve for x. 3x equals 72 minus 3 equals 69, so x equals 69 over 3 equals 23.

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List the integers. x equals 23, so the integers are 23, 24, 25.

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So the answer is The integers are 23, 24, 25.

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Writing every integer in terms of the smallest one turns the sentence into one linear equation, 3x plus 3 equals 72.

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23 plus 24 plus 25 equals 72, which checks out.

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Each integer differs from the next by 1, which checks out.