A grocer wishes to blend two different coffee brands because he wants to make a blend of 480 pounds to sell at $2.68 a pound. If he uses a brand of coffee worth $2.50 a pound with another brand worth $2.80 a pound, how many pounds of each does he use?

Accepted Solution

Answer:192 pounds of $2.5 brand288 pounds of $2.8 brandStep-by-step explanation:From the information we can write an expression that relates the two brands the total pounds of coffee the grocer wants to see. Let x be pounds of the coffee brand 1 and y be pounds of the coffee brand 2.Equation 1:[tex]480=x+y[/tex]We know that the price of will be equation 2:[tex]480*2.68=2.5*x+2.8*y[/tex]Two equations and two unknowns we can solve for x and y:[tex]x=480-y[/tex]Substitute into the second equation:[tex]480*2.68=2.5*(480-y)+2.8*y[/tex][tex]1286.4=1200-2.5*y+2.8*y[/tex][tex]y=86.4/0.3=288[/tex]Therefore he uses 288 pounds of brand two at $2.80 and 480-288=192 pounds of brand 1 at $2.50