The average of a set of 7 integers is 24. When an 8th number is included in the set, the average of the set increases to 31. What is the 8th number?

Question

Please He4lp!

Answer 1

Taking the average of a set of numbers allows us to generalize about each individual number when we don't actually know what the individual numbers are (and sometime even when we do know). So in this case we generalize that each individual number in the set of 7 numbers is 24. Therefore the sum of the 7 numbers is 7 * 24 which is 168. Since we know that the new average after adding an eighth number to the original group of 7 numbers is 31, we can again generalize that that each individual number in the set of 8 numbers is 31. So the sum of the new set of 8 numbers is 8 * 31 = 248. The difference between the sums of the two sets of numbers is 248 - 168 = 80. Since the difference between the sums of the two sets is 80 and there has been just one number added to the larger set, then the eighth number must be 80.

Answer 2

Its very easy to calculate.

Step 1 - Average of 7 numbers is 24 so the sum of those 7 numbers is going to be: 

7*24 = 168

step 2 - when 8th number is added the new average became 31. So the sum of all the 8 numbers is going to be:

 

8*31 =248

step 3 - Now to find the 8th number just subtract 168 from 248 i.e.-

248 -168 = 80

8th number is 80.

Please let me know if you need more depth explanation.