SOLUTION: Im trying to figure out how to write the equation for the following problem: find three consecutive even intergers such that one-forth of the first and one-seventh of the second pl

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Question 894700: Im trying to figure out how to write the equation for the following problem: find three consecutive even intergers such that one-forth of the first and one-seventh of the second plus one -half of the third is 13.
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Im trying to figure out how to write the equation for the following problem: find three consecutive even intergers such that one-forth of the first and one-seventh of the second plus one -half of the third is 13.
-------
Note:: Even numbers are always a multiple of 2.
1st:: 2(x-1)
2nd:: 2(x)
3rd:: 2(x+1)
---------
Equation:
(1/4)2(x-1) + (1/7)(2x) + (1/2)2(x+1) = 13
-------
Multiply thru by 28 to get:
14(x-1) + 8(x) + 28(x+1) = 28*13
-----
14x - 14 + 8x + 28x + 28 = 28*13
------
50x + 14 = 28*13
------
50x = 350
x = 7
------
1st:: 2(x-1) = 12
2nd:: 14
3rd:: 16
-------------------
Cheers,
Stan H.
=====================

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Im trying to figure out how to write the equation for the following problem: find three consecutive even intergers such that one-forth of the first and one-seventh of the second plus one -half of the third is 13.


Let 1st integer be F

Then, 2nd and 3rd are: F + 2, and F + 4, respectively

So, %281%2F4%29F+%2B+%281%2F7%29%28F+%2B+2%29+%2B+%281%2F2%29%28F+%2B+4%29+=+13

This translates to: F%2F4+%2B+%28F+%2B+2%29%2F7+%2B+%28F+%2B+4%29%2F2+=+13

7F + 4(F + 2) + 14(F + 4) = 13(28)}}} ------ Multiplying by LCD, 28

7F + 4F + 8 + 14F + 56 = 364

Collect and combine like-terms, and solve to determine F, the 1st integer. Then find other 2 (2nd & 3rd)

Then do a check!! 



If you need a complete and detailed solution, let me know!!



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