Question 269773
Let x = the number of lbs. of hazelnuts at $6.50 per pound and (60-x) = the number of lbs. of cashews at $4.50 per pound.
The mixture (the sum of these two) is to be 60 lbs at $5.10 per pound.
This can be expressed algebraically by:
6.5x+4.5(60-x) = 5.1(60) Simplify.
6.5x+270-4.5x = 306 Combine like-terms.
2x+270 = 306 Subtract 270 from both sides.
2x = 36 Divide both sides by 2.
x = 18
Jackie will need to mix 18 lbs. of hazelnuts @ $6.50 per pound with (60-18 = 42)lbs. of cashews @ $4.50 per pound to obtain 60 pounds of the mixture @ $5.10 per pound.