For 5 consecutive even integers, the sum of the first and third integer is 20 less than 3 times the fourth integer. What is the fifth integer?
The 5 integers: n, n+2, n+4, n+6, n+8.
n + (n+4) = 3(n+6) - 20,
n = 6.
n+8 = 6+8 = 14 = The 5th integer.
Let the middle integer have the value x. Then we are told that
(x-4) + x = 3(x+2)-20
Find x, and the 5th integer is x+4
Well, it seems like we've got some sneaky even integers playing mathematical games with us! Let's start solving this brain teaser, but remember to keep a clownish sense of humor along the way.
Let's call the first even integer "x". That means the second one is "x + 2", the third one is "x + 4", the fourth one is "x + 6", and the fifth one is "x + 8".
According to the problem, the sum of the first and third integers is 20 less than 3 times the fourth integer. So, we can write it down as:
(x) + (x + 4) = 3(x + 6) - 20
Let's simplify it a bit:
2x + 4 = 3x + 18 - 20
Now, let's solve for x:
2x - 3x = 2
-x = 2
x = -2
Now that we know x is -2, we can find the fifth integer by plugging it in:
x + 8 = -2 + 8 = 6
So, the fifth integer in our sequence of consecutive even integers is 6. Enjoy playing with numbers, my friend!
Let's break down the problem step-by-step:
Step 1: Define the integers
Let's assume that the first even integer is x. Since the problem states "consecutive even integers," the next four even integers would be x+2, x+4, x+6, and x+8.
Step 2: Translate the given information into an equation
According to the problem, the sum of the first and third integers (x and x+4) is 20 less than 3 times the fourth integer (3 * (x+6)).
(x + (x + 4)) = 3(x + 6) - 20
Simplifying the equation:
2x + 4 = 3x + 18 - 20
2x + 4 = 3x - 2
Step 3: Solve the equation
Subtract 2x from both sides of the equation to isolate the variable:
2x - 2x + 4 = 3x - 2 - 2x
4 = x - 2
Add 2 to both sides of the equation:
4 + 2 = x - 2 + 2
6 = x
So, the first even integer (x) is 6.
Step 4: Find the fifth integer
The fifth integer is x + 8, where x = 6.
Therefore, the fifth even integer is 6 + 8 = 14.
The fifth integer in the given sequence is 14.
To solve this problem, let's break it down step by step:
1. Let's assume that the first even integer is represented by "x". Since we are looking for 5 consecutive even integers, we can represent the remaining four integers as "x + 2", "x + 4", "x + 6", and "x + 8".
2. According to the problem, the sum of the first and third integer is 20 less than 3 times the fourth integer. We can express this mathematically as follows:
(x) + (x + 4) = 3 * (x + 6) - 20
3. Now we can solve the equation to find the value of "x":
2x + 4 = 3x + 18 - 20
Simplifying further:
2x + 4 = 3x - 2
Rearranging the equation:
2x - 3x = -2 - 4
-x = -6
Dividing both sides by -1:
x = 6
4. We have found that the first even integer, represented by "x", is 6. Now we can find the remaining four consecutive even integers:
x + 2 = 6 + 2 = 8
x + 4 = 6 + 4 = 10
x + 6 = 6 + 6 = 12
x + 8 = 6 + 8 = 14
5. Therefore, the fifth integer in the sequence is 14.
So, the fifth integer in the sequence of 5 consecutive even integers is 14.