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?
How many pounds of each does he use?
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\(x+y=400\\ y=400-x\\ 2.7x+3.2y=3\cdot400\\ 2.7x+3.2(400-x)=1200\\ 2.7x-3.2x=-1280+1200\\ -0.5x=-80\\ \color{blue}x=160\ \text{pounds a 2.70 \$}\\ \color{blue}y=240\ \text{pounds a 3.20 \$} \)
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