Question 970156: The mean of four consecutive even numbers is 15
The greatest of these numbers is?
The least of these numbers is?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve this, we need to set this word problem as a formula. The question says that we have 4 consecutive even numbers that when we take the mean of these 4 numbers, we get 15. So, let's rewrite this as follows:
Let's use x for the unknown numbers. So, the first number would be x. Now, the next consecutive even number would be 2 more than the first, so our second number would be written as x + 2. Our third number would be 2 more than the second number, which can be written as x + 4. Finally, our fourth number would be 2 more than the third number, which can be written as x + 6. To summarize, we have the following to represent each number:
Number 1: x
Number 2: x + 2
Number 3: x + 4
Number 4: x + 6
We also know that if we take the mean (the average) of those four numbers, our result will be 15. To take the average of 4 numbers, we add the 4 numbers together and divide by 4. So, our equation would like the following:
We now have an equation we can solve. First, we can multiply both sides of the equation by 4 so that we can get rid of the fraction. This results in:
x + x + 2 + x + 4 + x + 6 = 60
Next, combine like terms on the left side of the equal sign, giving us:
4x + 12 = 60
Then, subtract 12 from both sides, giving us:
4x = 48
Finally, divide both sides by 4, which will give us our value for x:
x = 12
So, we know that x is 12, which means that Number 1 is 12. Our second number is 2 more than that, so our second number is 14. Our third number is two more than the second number, which is 16. Our final number is 2 more than the third number, which is 18. We now have our four numbers in order from smallest to largest: 12 14 16 and 18
The greatest of these numbers is 18
The least of these numbers is 12
To verify all of this, do the following:
This results in 15, so our answer is correct.
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