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The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $15 per pound. The manager wishes to make a 75-pound mixture of both that will sell for $13 per pound. How many pounds of each should be used

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Answer:

  • 15 pounds of trail mix
  • 60 pounds of premium cashews

Explanation;

75 pounds of the mixture should be made so assuming the trail mix is x and the premium cashew is y, the following expression is formed;

x + y = 75

The selling price per pound is $13 so in total, sales should be;

= 75 * 13

= $975

5x + 15y = 975

Substitution can then be used;

x + y = 75

y = 75 - x

Then;

5x + 15y = 975

5x + 15 ( 75 - x ) = 975

5x + 1,125 - 15x = 975

-10x = -150

x = 15

y = 75 - 15

= 60

15 pounds of trail mix

60 pounds of premium cashews

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