You are watching: The mean of four consecutive even numbers is 15.
Click right here to watch ALL problems on Problems-with-consecutive-odd-even-integersQuestion 970156: The average of 4 consecutive also numbers is 15The greatest of these numbers is?The least of these numbers is? answer by josh_jordan(263)
(Show Source): You have the right to put this solution on her website! To deal with this, we need to set this word difficulty as a formula. The concern says the we have actually 4 consecutive also numbers that when we take the median of this 4 numbers, we acquire 15. So, let"s rewrite this as follows:Let"s use x because that the unknown numbers. So, the first number would be x. Now, the next consecutive even number would be 2 more than the first, therefore our second number would be composed as x + 2. Our 3rd number would certainly be 2 an ext than the second number, which have the right to be written as x + 4. Finally, our fourth number would certainly be 2 an ext than the 3rd number, which have the right to be created as x + 6. To summarize, we have actually the adhering to to represent each number:Number 1: xNumber 2: x + 2Number 3: x + 4Number 4: x + 6We additionally know that if us take the median (the average) that those four numbers, our result will it is in 15. To take it the median of 4 numbers, we include the 4 number together and divide by 4. So, our equation would favor the following:We now have actually an equation we can solve. First, we can multiply both political parties of the equation by 4 for this reason that we can remove the fraction. This results in:x + x + 2 + x + 4 + x + 6 = 60Next, combine like terms on the left side of the same sign, giving us:4x + 12 = 60Then, subtract 12 indigenous both sides, providing us:4x = 48Finally, divide both political parties by 4, i m sorry will give us our value for x:x = 12So, we recognize that x is 12, which means that Number 1 is 12. Our second number is 2 more than that, therefore our 2nd number is 14. Our 3rd number is two much more than the 2nd number, i m sorry is 16. Our last number is 2 an ext than the 3rd number, i m sorry is 18.
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We now have actually our 4 numbers in stimulate from the smallest to largest: 12 14 16 and also 18The greatest of these numbers is 18The least of this numbers is 12To verify all of this, do the following:This outcomes in 15, so our price is correct.