SOLUTION: The sum of three consecutive integers is 33 more than the least of the integers. Find the integers.

Question 105664: The sum of three consecutive integers is 33 more than the least of the integers. Find the integers.
Found 2 solutions by elima, bucky:
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
The sum of three consecutive integers is 33 more than the least of the integers. Find the integers.
x=first integer
x+1=second integer
x+2= third integer
========================
x+x+1+x+2=x+2+33
3x+3=x+35
3x-x=35-3
2x=32
x=16
so the integers are;
16,17,18
:)

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The three consecutive integers can be represented as:
.
x
x+1 and
x+2
.
The sum of these three is 3x + 3
.
If you take 33 away from this sum, it is to equal the least of the integers which is x.
So
.
3x + 3 - 33 = x
.
Subtract x from both sides and you get:
.
2x + 3 - 33 = 0
.
Now combine the +3 and -33 and you have:
.
2x - 30 = 0
.
Add 30 to both sides:
.
2x = 30
.
Solve for x by dividing both sides by 2 to get:
.
x = 15
.
So the answer is that the three integers are 15, 16, and 17.
.
RELATED QUESTIONS
The sum of three consecutive integers is 33 more than the least of the integers. Find... (answered by College Student)
the sum of three consecutive integers is 33 more than the least of the integers..find the (answered by jim_thompson5910)
the sum of 3 consecutive integers is 33 more than the least of the integers. find the... (answered by robertb)
The sum of three consecutive integers is 53 more than the least of the integers. Find the (answered by checkley77)
sum of four consecutive odd integers is three more than five times the least of integers. (answered by CubeyThePenguin)
sum of four consecutive odd integers is three more than five times the least of... (answered by CubeyThePenguin)
The sum of three consecutive integers is 47 less than the least of the integers. Find the (answered by midwood_trail)
The sum of four consecutive odd integers is three more than five times the least of the... (answered by CubeyThePenguin)
The sum of three consecutive odd integers is 16 more than the greatest of the integers.... (answered by Earlsdon)