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

1 Answer
Mar 28, 2018

Answer:

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#