How many pounds of raisins worth $1.50 per pound must be mixed with 10 pounds of peanuts worth $1.20 per pound to produce a mixture worth $1.40 per pound?

Your mixture of raisins and peanuts is worth $1.40/lb.

You can determine the pounds of raisins from the given information by creating an equation like this:

(lbs raisins)($1.50/lb) + (10lbs peanuts)($1.20/lb) = (lbs raisins + 10lbs peanuts)($1.40/lb)

which looks like this:
1.5r + 12 = 1.4r +14
r = 20

You need 20 lbs of raisins for your mixture.