Determine the number of pounds of nuts selling for $6 per pound and raisins selling for $3 per pound
that should be combined to create 60 pounds of a trail mix selling for $5 per pound.

For the mix you need 60 Ib of nuts and raisins, and 60 lb of mix will sell for $300.
Let x be the weight of nuts and y the weight of raisins needed for the mix.
Total weight = x+y = 60, so y = 60 - x
Total value = 6x + 3y = 300.  From the above, we can substitute the y for 60 - x:
Total value = 6x + 3(60 - x) = 300, which we can simplify to:
6x + 180 - 3x = 300, and simplify again to:
3x = 120, and again to:
x = 40.  We can now calculate y from the first equation y = 60 - x, so:
y = 20.
40 lb of nuts and 20 lb of raisins.  Check:
40 lb x $6/lb = $240, and 20 lb x $3/lb = $60, $240 + $60 = $300.