SOLUTION: If the second of three consecutive integers is subtracted from 105, the result is the sum of the first and third. What are the integers?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: If the second of three consecutive integers is subtracted from 105, the result is the sum of the first and third. What are the integers?      Log On


   

Question 1127022: If the second of three consecutive integers is subtracted from 105, the result is the sum of the first and third. What are the integers?
Found 3 solutions by josgarithmetic, MathLover1, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
first, n-1
second, n
third, n+1

105-n=%28n-1%29%2B%28n%2B1%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let three consecutive integers be x,%28x%2B1%29, and %28x%2B2%29
If the second of three consecutive integers is subtracted from 105, the result is the sum of the first and third:
105-%28x%2B1%29=x%2B%28x%2B2%29
105-x-1=x%2Bx%2B2
104-x=2x%2B2
104-2=2x%2Bx
102=3x
x=102%2F3
x=34-> first integer
%28x%2B1%29=35->second integer
%28x%2B2%29=36-> third integer

check:
105-%28x%2B1%29=x%2B%28x%2B2%29
105-35=34%2B36
70=70

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


You can simplify the required algebra using logical reasoning, knowing that, in three consecutive integers, the sum of the first and third is twice the second. So if x is the second number, the problem says

105-x+=+2x
105+=+3x
x+=+35

The middle number is 35; the integers are 34, 35, and 36.