A grocer wishes to blend two different coffee brands in order to make a blend of 400 pounds to sell at $3.00 a pound. If he uses a brand of coffee worth $2.70 a pound with another brand worth $3.20 a pound, how many pounds of each does he use?

Accepted Solution

Step-by-step explanation:Let's say x is the amount of $2.70/lb coffee and y is the amount of $3.20/lb coffee.The total amount is:x + y = 400The total worth is:2.70x + 3.20y = 3.00Γ—4002.7x + 3.2y = 1200Solving the system of equations through substitution:x = 400 - y2.7 (400 - y) + 3.2y = 12001080 - 2.7y + 3.2y = 12000.5y = 120y = 240x = 160The grocer uses 160 pounds of the $2.70/lb coffee and 240 pounds of the $3.20/lb coffee.