How many pounds of nuts selling for $6 per lb and raisins for $3 per lb should a person combine to obtain 150 lb of trail mix selling for $4 per lb?
##50## lb. of nuts and
##100## lb. of raisins.
Let ##n## represent the number of pound of nuts
and ##r## the number of pound of raisins.
We are told:
##color(white)(“XXX”)color(red)(n+r=150)##
Selling value (in dollars) of nuts in this combination: ##6n##
Selling value (in dollars) or raisins in this combination: ##3r##
Selling value (in dollars) of nuts and raisins in this combination: ##6n+3r##
but we are told that the selling value (in dollars)of the combination is to be ##($4)/”pound” xx 150 ” pounds”=$600##
So
##color(white)(“XXX”)color(blue)(6n+3r=600)##
##color(red)(n+r=150) rarr color(red)(r=150-n)##
Substituting this into ##color(blue)(6n+3r=600)##
##color(white)(“XXX”)color(blue)(6n+3(color(red)(150-n))=600##
##color(white)(“XXX”)3n+450=600##
##color(white)(“XXX”)3n=150##
##color(white)(“XXX”)color(green)(n=50)##
Substituting this back into ##color(red)(n+r=150)##
gives:
##color(white)(“XXX”)color(green)(r=100)##