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lialeee lialeee
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11 years ago
In preparation for the World Cup, a dietary supplement is proposed for the
      New Zealand All Whites soccer team. Altogether they are to have 1250 mg of
      vitamin D, 250 mg of selenium, and 700 mg of folic acid per day. This is to be
      accomplished by using three liquid food supplements A, B and C. A contains
      40 mg of vitamin D, 10 mg of selenium and 20 mg of folic acid per 100 cc; B
      contains 50 mg of vitamin D and 100 mg of folic acid per 100 cc; and C
      contains 100 mg of vitamin D, 20 mg of selenium and 50 mg of folic acid per
      100 cc. How many cc of each of the three foods A, B and C should the team
      receive each day?
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11 years ago
Let A=amount of "A" taken, B=amount of "B" taken, and C=amount of "C" taken.

40A+50B+100C=1250
10A+0B+20C=250
20A+100B+50C=700

This can be solved by normal systems of equations methods (substitution or elimination).  It is easiest to solve using matrices.  You can either do this in Excel using the matrix formulas (MINVERSE and MMULT, which have to be entered as an array formula - quite weird if you've never done that before) or by using a calculator.

I get A=5, B=1, C=10.  But these are just units of A, B, and C.  Since each "unit" is 100 cc, we need A=500cc, B=100cc, and C=1000cc.
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