SOLUTION: 2. The sum of three consecutive even integers is 114 a. Define a variable for the smallest integer b. Define variables to represent the 2nd and 3rd integers c. Write an equat

Algebra ->  Expressions-with-variables -> SOLUTION: 2. The sum of three consecutive even integers is 114 a. Define a variable for the smallest integer b. Define variables to represent the 2nd and 3rd integers c. Write an equat      Log On


   

Question 96827: 2. The sum of three consecutive even integers is 114
a. Define a variable for the smallest integer
b. Define variables to represent the 2nd and 3rd integers
c. Write an equation for the sum of the tree consecutive even integers.
d. Solve the equation to find the three even integers.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) let x=smallest integer

b) 2nd integer: y=x%2B2, 3rd integer: z=x%2B4 (remember consecutive even integers increment by 2 each time)


c) Sum:
x%2By%2Bz=114

x%2B%28x%2B2%29%2B%28x%2B4%29=114 Plug in y=x%2B2 and z=x%2B4


d)
x%2Bx%2B2%2Bx%2B4=114 Remove the parenthesis


3x%2B6=114 Combine like terms on the left side


3x=114-6Subtract 6 from both sides


3x=108 Combine like terms on the right side


x=%28108%29%2F%283%29 Divide both sides by 3 to isolate x



x=36 Divide

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Answer:
So first number is x=36



Now plug in x=36 into the 2nd and 3rd number equations


2nd number: 36%2B2=38
3rd integer: 36%2B4=40


So the 3 numbers are

36, 38, 40



Check:

36%2B38%2B40=114 Add up the 3 numbers. Their sum should equal 114

114=114 works