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300 is the sum of 15 consecutive even positive integers. What is the greatest even positive integer among them? show your work.

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  • 4 weeks ago

    300 is the sum of 15 consecutive even positive integers. What is the greatest even positive integer among them? show your work.

    x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) + (x+ 9) + (x+10) + (x+11) + (x+12) + (x+13) + (x+14) = 300

    15 x + 105 = 300

    15 x =195

    x = 13

    x + 14 = 13 + 14 = 27

    greatest among them is 27

  • 1 month ago

    We have x, x + 2, x + 4, x + 6,....to 15 terms

    i.e. 15x + (0 + 2 + 4 + 6 +...) to 15 terms

    or, 15x + 210 = 300

    => x = 6

    The 15th term is x + 28, hence 34

    :)>

  • 1 month ago

    Let x be the *middle* even number. You'll have 7 even numbers on either side. Add them all up to get 300:

    (x - 14) + (x - 12) + (x - 10) + ... + (x - 2) + x + (x + 2) + ... + (x + 10) + (x + 12) + (x + 14) = 300

    As you can see, if you add that up you find that the *middle* number is the average of all these numbers. That's because all the numbers cancel out and you get:

    15x = 300

    x = 300/15

    x = 20

    That's the middle number and the largest consecutive even number is 14 more than that.

    20 + 14 = 34

    Double-check:

    6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 = 300

    Answer:

    34

  • 1 month ago

    The sum from 1 to 15 is 15 * 16 / 2 = 120

    The remaining 300 - 120 = 180 has to be distributed across the 15 numbers, so we add 180 / 15 = 12 to each number, giving a range from 13 to 27.

    So the greatest even positive integer among them is 26.

    • Φ² = Φ+1
      Lv 7
      1 month agoReport

      Thank you roderick - yes, I missed the word "even" in the question. Thank you for pointing that out. There are plenty of people out there who will thumbs-down an answer, but don't have the courage or decency to string a few words together in explanation. Feel free to give this a thumbs down.

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  • 1 month ago

    300 is the sum of 15 consecutive even positive integers.

    15/2(x + x + 14) = 300

    15(x + 7) = 300

    x + 7 = 20

    The greatest even positive integer among them is 26.

    • roderick_young
      Lv 7
      1 month agoReport

      I didn't downvote, because your answers are usually good, but I don't follow your logic. Maybe there's a different way of interpreting this word problem?

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