SOLUTION: The sum of three consecutive even numbers is 150. Find the numbers. Please help! Thanks!

Question 156715: The sum of three consecutive even numbers is 150. Find the numbers.
Please help!
Thanks!
Found 5 solutions by josmiceli, nerdybill, oscargut, checkley77, jim_thompson5910:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
If I call the 1st number , then the next number must be
, and the 3rd number will be

The numbers are 49, 50, and 51
check answer:

OK
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
The sum of three consecutive even numbers is 150. Find the numbers.
.
Let x = 1st consecutive even number
then
x+2 = 2nd consecutive even number
x+4 = 3rd consecutive even number
.
x + (x+2) + (x+4) = 150
3x + 6 = 150
3x = 144
x = 48 (1st consecutive even number)
x+2 = 50 (2nd consecutive even number)
x+4 = 52 (3rd consecutive even number)
Answer by oscargut(2103)   (Show Source): You can put this solution on YOUR website!
Let n,n+2 and n+4 consecutive even numbers
then

then

then

then

Then
Numbers are: 48,50 and 52

Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
x+(x+2)+(x+4)=150
3x+6=150
3x=150-6
3x=144
x=144/3
x=48 the smallest even number.
48+2=50 the middle even number
48+4=52 the larest even number.
Proof:
48=50=52=150
150=150
SHORTCUT:
150/3=50 THIS IS THE MIDDLE NUMBER (X+2)

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
"consecutive even numbers" are integers such as 2, 4, 6, 8, 10, etc. Algebraically, they follow the pattern , , , etc

So if "The sum of three consecutive even numbers is 150", then the equation is

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

--------------------------

Go back to the expression that represents the first number

Plug in

Multiply. So the first number is 48

---------------------------

Go back to the expression that represents the second number

Plug in

Multiply.

Add. So the second number is 50

---------------------------

Go back to the expression that represents the third number

Plug in

Multiply.

Add. So the third number is 52

==============================

Answer:

So the three consecutive even numbers is 48, 50, and 52

Check:

1)
they are consecutive even integers...check

2)
48+50+52=150
150=150 ... works

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