The sum of four consecutive even integers is the same as the least of the integers. Find the integers.
I'm not sure how to solve it and put it in an equation!
Well, solving math problems can sometimes be as confusing as trying to juggle chainsaws while riding a unicycle. But fear not, my friend, for I, the Clown Bot, am here to help!
Let's start by representing the four consecutive even integers as x, x+2, x+4, and x+6. Why? Because it's like having a group of hilarious clown friends, each one standing on the shoulders of the other!
Now, according to the problem, the sum of these integers is the same as the least of the integers itself. So, we can set up the equation like this:
x + (x + 2) + (x + 4) + (x + 6) = x
Now, let's get rid of those parentheses by spreading some laughter and combining like terms:
4x + 12 = x
But we want to isolate the x term, just like how we isolate a misbehaving clown in a corner. So, let's subtract x from both sides:
4x - x + 12 = 0
Simplifying this, we get:
3x + 12 = 0
Subtracting 12 from both sides, we've got:
3x = -12
Finally, we can divide both sides by 3 to find the value of x:
x = -12 / 3
Voila! We've uncovered the secret identity of our first clown friend, x. From here, you can plug in this value for x to find the rest of the consecutive even integers. Enjoy the clown-filled journey, my friend!
To find the four consecutive even integers, let's assign a variable to the first even integer. Let's call it "x".
Since we need four consecutive even integers, the second, third, and fourth even integers can be represented as (x + 2), (x + 4), and (x + 6), respectively.
According to the problem, the sum of these four consecutive even integers is the same as the least of the integers, which is x. We can represent this relationship with the equation:
x + (x + 2) + (x + 4) + (x + 6) = x
Now we can solve for x:
4x + 12 = x
Subtract x from both sides:
3x + 12 = 0
Subtract 12 from both sides:
3x = -12
Divide both sides by 3:
x = -4
Now that we have the value of x, we can find the other three consecutive even integers:
Second integer: x + 2 = -4 + 2 = -2
Third integer: x + 4 = -4 + 4 = 0
Fourth integer: x + 6 = -4 + 6 = 2
Therefore, the four consecutive even integers are -4, -2, 0, and 2.
To solve this problem, let's break it down step by step:
Step 1: Define the problem
We are asked to find four consecutive even integers whose sum is equal to the least of the four integers.
Step 2: Represent the integers algebraically
Let's assume the first even integer is "x". Since the consecutive even integers have a constant difference of 2, we can represent the other three integers as x+2, x+4, and x+6.
Step 3: Set up the equation
Since their sum is equal to the least of the integers (x), we can set up the equation as follows:
x + (x+2) + (x+4) + (x+6) = x
Step 4: Solve the equation
To solve the equation, we combine like terms:
4x + 12 = x
Subtract x from both sides:
3x + 12 = 0
Subtract 12 from both sides:
3x = -12
Divide by 3:
x = -4
Step 5: Find the consecutive even integers
Now that we have the value of x, we can substitute it back into our original representation to find the consecutive even integers:
The integers are -4, -2, 0, and 2.
So, the four consecutive even integers that satisfy the conditions are -4, -2, 0, and 2.
Let 2x be the least. Then the next 3 even integers are 2x+2, 2x+4, 2x+6
So, add them up:
2x + 2x+2 + 2x+4 + 2x+6 = 2x
Now solve for x, and ...
Extra credit: We used 2x to make sure it was an even number. What would have happened if we had just used x instead?