Question

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

Answer 1

See a solution process below:

Explanation:

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

`a = s/n` Where

• `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 `s` we can find the some of the numbers:

`6 = s/7`

`color(red)(7) xx 6 = color(red)(7) xx s/7`

`42 = cancel(color(red)(7)) xx s/color(red)(cancel(color(black)(7)))`

`42 = s`

`s = 42`

If the average is to increase by 10, then the new average would be: `6 + 10 = 16`

The count of numbers would increase to `8`

And if we call the value of the new number added in `w`, then the sum of the set of numbers is: `42 + w`

Substituting this into the formula for average and solving for `w` gives:

`16 = (42 + w)/8`

`color(red)(8) xx 16 = color(red)(8) xx (42 + w)/8`

`128 = cancel(color(red)(8)) xx (42 + w)/color(red)(cancel(color(black)(8)))`

`128 = 42 + w`

`128 - color(red)(42) = 42 - color(red)(42) + w`

`86 = 0 + w`

`86 = w`

`w = 86`

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

`a = (42 + 86)/8`

`a = 128/8`

`a = 16`