Thursday, November 25, 2010

Number Problem 10 Solution

This is number problem 10 solution which read:

"Find 3 consecutive even integers such that 4 times the first is decreased by the second is 12 more than twice the third. " Ok I'm not understading the "is decreased by the" part so I assume it was a typo and you just meant "Find 3 consecutive even integers such that 4 times the first is 12 more than twice the third. "
 
ok 3 consecutive even integers would b x, x + 2, and x + 4

4 times the 1st would be just 4x and is equal to 12 more than twice the 3rd which would be (x + 4) * 2 + 12

which is...  4x = (x+4)*2 + 12

4x = 2x + 8 + 12

2x = 20

x = 10  So the answer would be 10, 12, 14   to check  4(10)  =  (14)*2 + 12

40 = 28 + 12

40 = 40

16 comments:

  1. maybe it should be this way
    x=1st integer
    x+2= 2nd integer
    x+4= 3rd integer

    4x-x+2=12+(x+4)2
    3x+2=12+2x+8
    3x+2=20+2x
    3x-2x=20-2
    x = 18

    but im not really sure w/ dis one

    ReplyDelete
    Replies
    1. it can't be 18 cuz

      4*18=72

      18+4=22
      22*2=44
      44+12=56

      72 doesn't=56

      Delete
  2. The question doesn't make sense as written i think it was a typo so i just solved the question i think they meant to say.

    ReplyDelete
  3. This question is bad. I got a different answer to both the poster and the commenter above.

    x, x + 2, x + 3

    "4 times the first is decreased by the second" -

    4x - (x + 2)

    "is 12 more than twice the third"

    4x - (x + 2) = 2(x + 4) + 12

    4x - x - 2 = 2x + 8 + 12

    3x - 2 = 2x + 20

    x = 22

    Validating -

    4(22) - (22 + 2) = 2(22 + 4) + 12

    88 - 22 - 2 = 44 + 8 + 12

    64 = 64

    Hope this helps.
    - Damon

    ReplyDelete
  4. "4 times the first is decreased by the second" --- -is too vague -- in my problem i corrected it to what i believe the poster meant to ask it and makes more sense as a question and thus the answer but thanks for your input though...

    ReplyDelete
  5. Wrong translation sir...

    ReplyDelete
  6. this site is the best

    ReplyDelete
  7. I agree with the one who answered 22, 24, 26 coz we've got the same answer and checking, re stating the problem as "Find 3 consecutive even integers such that 4 times the 1st decreased by the second is 12 more than twice the 3rd.

    ReplyDelete
  8. I agree with anonymous' translation as well. --- That's probably what was meant. I answered a different problem, but I will keep that and people can reference both that way. Thanks for the input!

    ReplyDelete
  9. Thanks for the example. It really helps.

    ReplyDelete
  10. there's nothing wrong with the problem

    here's my solution...

    4x - (x+2) = 12 + 2(x+4)

    just use algebra to solve it and you'll get these answers:

    x = 22
    x+2 = 24
    x+4 = 26

    ReplyDelete
  11. let x be the first integer
    x+2 second integer
    x+4 third integer

    4x-x+2 = 2(x+4) + 12
    3x+2 = 2x+8+12
    3x+2 = 2x+20
    3x-2x = 20-2
    x = 18

    Checking:
    x= 18
    x+2= 20
    x+4= 22
    4x-x+2 = 2(x+4)+12
    4(18)-20 = 2(22)+12
    72-20 = 44+12
    52 = 52

    Therefore the numbers are 18, 20 and 22

    ReplyDelete


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