SOLUTION: the sum of three consecutive integers is 26 more than the smallest integer

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Question 933235: the sum of three consecutive integers is 26 more than the smallest integer
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of three consecutive integers is 26 more than the smallest integer
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1st:: x-1
2nd:: x
3rd:: x+1
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Sum = 3x = (x-1)+26
3x = x+25
2x = 25
x = 12.5
----
Not an integer.
No solution.
Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
by definition: Integers are like whole numbers, but they also include negative numbers, but still no fractions allowed!
let the first integer be x%2B1, the second is x%2B2 and the third is x%2B3
the smallest integer is x%2B1
if the sum of three consecutive integers is 26 more than the smallest integer, then we have:
%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29=x%2B26...solve for x
x%2B1%2Bx%2B2%2Bx%2B3=x%2B26
3x%2B3=x%2B26
3x-x=26-3
2x=23
x=23%2F2 it is not an integer which is a number with no fractional part
let’s try with
three consecutive even integers ---> x ,%28x+%2B+2%29, and +%28x+%2B+4%29+
x+%2B+%28x+%2B+2%29+%2B+%28x+%2B+4%29=x%2B26
x+%2B+x+%2B+2+%2B+x+%2B+4=x%2B26
3x+%2B+6=x%2B26
3x+-x=26-6
2x=20
x=10
your integers are: highlight%2810%29,highlight%2812%29, and highlight%2814%29
try also three consecutive odd integers are of the form:
%282x%2B1%29%2B+%282x%2B3%29%2B+%282x%2B5%29=%282x%2B1%29%2B26
2x%2B1%2B+2x%2B3%2B+2x%2B5=2x%2B1%2B26
6x%2B9=2x%2B27
6x-2x=27-9
4x=18
x=18%2F4
x=9%2F2....it is not an integer either
so, you must have three consecutive even integers to have a solution