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Word problemsArithmeticMiddle schoolabout 1:29

The sum of three consecutive integers is 72. What is the smallest?: animated lesson

A narrated, step-by-step word problems video lesson with captions. Final answer: The integers are 23, 24, 25.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.6 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    The sum of three consecutive integers is 72. What is the smallest?
  2. 2. Steps, part 1
    1. Read the problem
    2. Name the integers
    3. 3x+3=723x + 3 = 72
      Write the equation
    4. Combine like terms
  3. 3. Steps, part 2
    1. x=693=23x = \frac{69}{3} = 23
      Solve for x
    2. List the integers
  4. 4. The answer
    The integers are 23, 24, 25\text{The integers are 23, 24, 25}

    3x + 3 = 72 → x = 23

  5. 5. Check
    • 23 + 24 + 25 = 72 ✓
    • Each integer differs from the next by 1 ✓

Transcript

The problem. Here is the problem: The sum of three consecutive integers is 72. What is the smallest? 3 consecutive integers with sum 72. 3 consecutive integers with sum 72.

Steps, part 1. Read the problem. 3 consecutive integers with sum 72. 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). Write the equation. x plus (x plus 1) plus (x plus 2) equals 72. 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.

Steps, part 2. Solve for x. 3x equals 72 minus 3 equals 69, so x equals 69 over 3 equals 23. List the integers. x equals 23, so the integers are 23, 24, 25.

The answer. So the answer is The integers are 23, 24, 25. Writing every integer in terms of the smallest one turns the sentence into one linear equation, 3x plus 3 equals 72.

Check. 23 plus 24 plus 25 equals 72, which checks out. Each integer differs from the next by 1, which checks out.

About word problems

Turn everyday situations about prices, speed, ages and interest into equations and solve them.

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