Question

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?

Answer 1

`50` lb. of nuts and
`100` lb. of raisins.

Explanation:

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)`