SOLUTION: find the set of three consecutive even integers whose sum is 93

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: find the set of three consecutive even integers whose sum is 93      Log On


   

Question 507901: find the set of three consecutive even integers whose sum is 93
Found 3 solutions by oberobic, josmiceli, gsmani_iyer:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
3 consecutive even integers could be x, y, z
but then you'd have 3 unknowns
.
it is better to define them
x
x+2
x+4
.
now you have 1 unknown and given they sum to 93, you can define 1 equation
.
x +x+2 +x+4 = 93
.
3x +6 = 93
.
3x = 87
.
x = 29, which is NOT an even integer
.
x+2 = 31
.
x+4 = 33
.
So, there are three consecutive odd integers that sum 93 are 29, 31, and 33.
.
BUT there are NOT three consecutive even integers that sum to 93.
.
Done.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the integers +n+, +n+%2B+2+, and +n%2B4+
given:
+n+%2B+n+%2B+2+%2B+n+%2B+4+=+93+
+3n+%2B+6+=+93+
+3n+=+87+
+n+=+29+
+n+%2B+2+=+31+
+n+%2B+4+=+33+
and
+29+%2B+31+%2B+33+=+93+
These are 3 consecutive ODD integers. There is no way
that 3 even integers can add up to 93, because any
sum of even numbers is even, and 93 is odd.

Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!

Sum of even integers can never be an odd integer irrespective of no. of integers.
I hope it is three consecutive odd integers. They are 29, 31, 33. i.e.
A = {29, 31, 33}. I have not explained how I got these. Because you check up with your question. If it is odd integers, contact me gsmani9@yahoo.com.
All the best.