Question 418731
I can work this one at http://vyew.com/room#/365877/algebra.com if you want or you can wait and I'll answer it shortly through here.

let x=pounds of peanuts
y=pounds of cashews

then x+y=14 since they have to add up to be 14 pounds.
3.50x+7.50y=81

Now solve using substitution or elimination.  Substitution is likely easier in this case.
x=14-y
3.50(14-y)+7.50y=81
49-3.5y+7.5y=81
49+4y=81
4y=32
y=8 pounds
x+y=14
x+8=14
x=6 pounds
so he should buy 6 pounds of peanuts and 8 pounds of cashews.