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

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Answer 1 · 2017-02-23T06:29:08

The two numbers are $38.25$ and $44$

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 $44$