# Average of 7 numbers is 6.What is 8th no. to be added if the average increases by 10 ?

##### 1 Answer

See a solution process below:

#### Explanation:

The formula for the average of a set of numbers is:

#a# is the average of the numbers. We know from the problem the average of the first 7 numbers is#6# #s# is the sum of the set of numbers. We need to solve for this to answer the questions.#n# is the count of numbers in the set of number we are averaging. We know from the problem the count of numbers in the set is#7#

Substituting and solving for

If the average is to increase by 10, then the new average would be:

The count of numbers would increase to

And if we call the value of the new number added in

Substituting this into the formula for average and solving for

The eight number added in to make an average of 16 would be **86**