Date: Wed, 21 Apr 1999 18:25:06 EDT
Subject: precalculus portfolio for student

Could you please show me how to answer this precalculus problem. I am a student in the secondary level.

Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of $13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of $16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of $25.09. Alice buys 5 qts. of milk, 6 oranges, 2 dozen apples, 3.25 lb. of ground beef, and 4 bags of mixed vegetables, for a total of $21.06. Joan bought 1 qt. of milk, 3 oranges, 5 apples, 4 lb. of ground beef, and 15 lb of potatoes, for a total of $13.77. Bill bought 2 qt. of milk, 4 oranges, 8 apples, 3.5 lb. of ground beef, 9 lb. of potatoes, and 3 bags of mixed vegetables, for a total of $17.47. Assume that the price of each item does not change as the number of each item varies. Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables.

The answers to this question are .59 for a qt. of milk, .27 for one orange, .19 for an apple, 1.88 for 1 lb. of ground beef, .26 for a pound of potatoes, and 1.59 for a bag of mixed vegetables. I'd like to know how you arrive at these answers through your work. Thank you very much.


You first need standard units for each item so let

  • M be the amount of milk in quarts
  • O be the number of oranges
  • A be the number of apples
  • B be the amount of ground beef in pounds
  • P be the amount of potatos in pounds
  • V be the number of bags of mixed vegetables
Now write an equation for each shopper, for example for Joanne

8M + 12O + +8A + 2B + 0P + 0V = 13.42

If you do this for each shopper you will have eight equations in eight unknowns which you can then solve.


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