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)##