SOLUTION: the modern grocery has cashews that sell for $3.50 a pound and peanuts that sell for $2.00 a pound. how much of each must Alberts, the grocer, mix to get 60 pounds of mixture that

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the modern grocery has cashews that sell for $3.50 a pound and peanuts that sell for $2.00 a pound. how much of each must Alberts, the grocer, mix to get 60 pounds of mixture that       Log On


   



Question 12517: the modern grocery has cashews that sell for $3.50 a pound and peanuts that sell for $2.00 a pound. how much of each must Alberts, the grocer, mix to get 60 pounds of mixture that he can sell for $3.00 per pound. Express the problem as a system of linear equations and solve using the method of your choice to find the solution.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let C = the required number of lbs of cashews.
Let P = the required number of lbs of peanuts.
1) Express as a system of linear equations:
a) %283.50%29C+%2B+%282.00%29P+=+3.00%2860%29 and
b) C+%2B+P+=+60
2) Solve: Rewrite equation b) as: P+=+60+-+C and substitute into equation a) and solve for P.
a) %283.50%29C+%2B+%282.00%29%2860+-+C%29+=+3.00%2860%29 Simplify and solve for C.
3.5C+%2B+120+-+2C+=++180
1.5C+%2B+120+=+180
1.5C+=+60
C+=+40 40 lbs of cashews are required.
P+=+60+-+C
P+=+60+-+40
P+=+20 20 lbs of peanuts are are required.