Answer: 37, 38, and 39
Step-by-step explanation: This problem states that the sum of 3 consecutive integers is 114 and it asks us to find the integers.
3 consecutive integers can be represented as followed.
X ⇒ first integer
X + 1 ⇒ second integer
X + 2 ⇒ third integer
Since the sum of our 3 consecutive integers is 114, we can set up an equation to represent this.
X + X + 1 + X + 2 = 114
We can simplify on the left side by combining the X's and the numbers.
3x + 3 = 114
-3 -3 ← subtract 3 from both sides of the equation
3x = 111
÷3 ÷3 ← divide both sides of the equation by 3
X = 37
X ⇒ first integer = 37
X + 1 ⇒ second integer = 38
X + 2 ⇒ third integer = 39
Therefore, our 3 consecutive integers are 37, 38, and 39.
Answer:
Since your question asks for "three consecutive even integers" you can call them as follows:
x1 = first even integer
x2 = second even integer
x3 = third even integer
Since you know they're both consecutive and even, you know that:
x2 = x1 + 2
x3 = x2 + 2
This is because there's always a difference of 2 between consecutive even integers. Take a look at these examples:
6, 8, 10
102, 104, 106
514, 516, 518
No matter what the even integers are, as long as they're consecutive, they're spaced out by 2 each.
You know that the sum of your even integers adds up to 114, so:
x1 + x2 + x3 = 114
But since x3 = x2 + 2
x1 + x2 + (x2 + 2) = 114
And since x2 = x1 + 2
x1 + (x1 + 2) + ((x1 + 2) + 2) = 114
So your final equation will be:
x1 + x1 + 2 + x1 +2 + 2 = 114
3x1 + 6 = 114
3x1 = 108
x1 = 36
x2 = x1 + 2
x2 = 36 + 2 = 38
x3 = x2 + 2
x3 = 38 + 2 = 40
So your consecutive even integers are:
36, 38, and 40
If you add these all together you get:
36 + 38 + 40 = 114. So you know you did it correctly.
Hope this helps.
