SOLUTION: Three consecutive integers have a sum of 81 . Find the integers.

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Question 1088508: Three consecutive integers have a sum of
81
. Find the integers.
Found 3 solutions by ikleyn, math_helper, MathTherapy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let "x" will be an unknown middle number.

Then the three numbers are (x-1), x and (x+1).

You are given that 

(x-1) + x + (x+1) = 81,    or, which is the same,

3x = 81.


Hence, x =  = 27.


So, your numbers are 26, 27 and 28.

Solved.


Lesson to learn from this solution: 

     If you are given the sum of three consecutive integer numbers, the middle number is ONE THIRD of the sum.

     It is ALWAYS TRUE and may help you to solve similar problems MENTALLY.


Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Let a=smallest of the 3 integers
a + (a+1) + (a+2) = 81
3a + 3 = 81
3a = 78 —> a = 26
—
Ans: The three numbers are 26, 27, and 28
Check: 26+27+28 = 81 (ok)
————
Another method. Since the integers are consecutive, 3 times the average (which will be a+1) of the three numbers will be 81:
3(a+1) = 81
a+ 1 = 27
a = 26 —> the same answer 26, 27, 28 is obtained.
[ This method works for other evenly spaced integer problems, this particular problem has them spaced one apart. Just be sure to check your work by checking your answer. ]
————


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

Three consecutive integers have a sum of
81
. Find the integers.


 

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