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):
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):
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
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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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