The average of two numbers is 41.125, and their product is 1683. What are the numbers?

1 Answer
Feb 23, 2017

The two numbers are #38.25# and #44#

Explanation:

Let the numbers be #a# and #b#.

As their average is #(a+b)/2#, we have #(a+b)/2=41.125#

or #a+b=41.125xx2=82.25#

or #a=82.25-b# i.e. the numbers are #(82.25-b)# and #b#

As the product of numbers is #1683#, therefore

#b(82.25-b)=1683#

or #82.25b-b^2=1683#

or #329b-4b^2=6732# - multiplying each term by #4#

i.e. #4b^2-329b+6732=0#

and using quadratic formula #b=(329+-sqrt(329^2-4xx4xx6732))/8#

= #(329+-sqrt(108241-107712))/8=(329+-sqrt529)/8#

= #(329+-23)/8#

i.e. #b=352/8=44# or #b=306/8=153/4=38.25#

ans #a=82.25-44=38.25# or #a=82.25-38.25=44#

Hence the two numbers are #38.25# and #44#