SOLUTION: find three consecutive even integers such that the sum of the smallest and 3 times the second is 38 more than twice the third.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: find three consecutive even integers such that the sum of the smallest and 3 times the second is 38 more than twice the third.      Log On


   



Question 707693: find three consecutive even integers such that the sum of the smallest and 3 times the second is 38 more than twice the third.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Equation 1: B+=+A+%2B+2
Equation 2: C+=+A+%2B+4
Equation 3: A+%2B+3B+=+2C+%2B+38
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Note that B & C are written in terms of A. Substitute their values into equation 3.
Equation 3: A+%2B+3B+=+2C+%2B+38
A+%2B+3%2A%28A+%2B+2%29+=+2%2A%28A+%2B+4%29+%2B+38
Multiply through
A+%2B+3A+%2B+6+=+2A+%2B+8+%2B+38
Combine like terms
4A+%2B+6+=+2A+%2B+46
Subtract 6 from both sides
4A+=+2A+%2B+40
Subtract 2A from both sides
2A+=+40
Divide both sides by 2
highlight%28A+=+20%29
Now plug 20 into equations 1 & 2 for A.
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Equation 1: B+=+A+%2B+2
B+=+%2820%29+%2B+2
highlight_green%28B+=+22%29
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Equation 2: C+=+A+%2B+4
C+=+%2820%29+%2B+4
highlight%28C+=+24%29