Question 44145
Let us suppose that the Merchant mixed 'x' lbs of the $9 beans with 'y' lbs of $12 beans.


Hence, he created (x+y) lbs of mixture.
Given, total 100 lbs of the mixture is produced.
So, x + y = 100 _________(1)


Therefore, the cost of (x+y) lbs of the mixture = $(9x+12y).
Hence, the cost of 1 lb of the mixture = ${{{(9x+12y)/(x+y)}}}.
Given, cost of 1 lb the mixture = $11.25.
So, {{{(9x+12y)/(x+y) = 11.25}}}
or {{{(9x+12y)=11.25(x+y)}}}
or {{{12y - 11.25y = 11.25x - 9x}}}
or {{{0.75y = 2.25x}}}
or {{{y = 2.25x/0.75}}}
or y = 3x ________(2)


Substituting the value of 'y' from (2) in (1) we have
x + 3x = 100
or 4x = 100
or x = {{{100/4}}}
or x = 25


Substituting, x = 25 in (2), y = {{{3*25}}} = 75


Hence, 25 lbs of the $9 beans is to be mixed with 75 lbs of $12 beans to serve the reqd. purpose.