Question 970156
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:


{{{(x+x+2+x+4+x+6)/4=15}}}


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:


{{{(12+14+16+18)/4}}}


This results in 15, so our answer is correct.