Question 184857
Avis Proctor works at a gourmet delicatessen. She is preparing a cheese tray for a large reception. She is using some cheeses that sell for $8 per lb and others that sell for $12 per lb. How many pounds of cheese at each price should she use in the order for the mixed cheeses on the tray to weigh 56 lb and sell for $10.50 per lb?
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Quantity Equation: x + y = 56
Value Equation...:8x + 12y = 10.5*56
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Modify to prepare for elimination:
8x + 8y  = 8*56
8x + 12y = 10.5*56
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Subtract 1st from 2nd to solve for "y":
4y = 2.5*56
y = 2.5*14
y = 35 (# of lbs of $12 cheese in the mixture)
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Substitute into x+y = 56 to solve for "x":
x + 35 = 56
x = 21 (# of lbs of $8 cheese in the mixtue)
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cheers,
Stan H.