Applications of Systems of Equations

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Applications of Systems of Equations
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• Together, two scientists devoted 28 hours to
  testing water samples for pollution. If the
  first scientist spent 4 hours more than the
  second, how many hours did each spend?

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• Find two numbers where their sum is 42 and their
  difference is 14.

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• Find two numbers where their sum is 40, and one
  number is three times the other.

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• The manager of a theater knows that 900 tickets
  were sold for a certain performance. If
  orchestra tickets sold for 3 each and balcony
  tickets sold for 2 each, and if the total
  receipts were 2300, how many of each kind of
  ticket were sold?

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• An engineer worked for 6 days and an assistant
  worked for 7 days investigating the effects of
  manufacturing processes which contribute to air
  pollution. Together they received a salary of
  4500. The following week, the engineer worked 5
  days and the assistant worked 3 days for a
  combined salary of 2900. Find the daily wages
  of each.

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• Marsha scored 85 on her first test in algebra.
  The average of her first two tests was 9 less
  than her score on the third test. The average of
  all three tests was 83. What did she score on
  the second and third tests?

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• To join a nature study club, there is an
  initiation fee and monthly dues. At the end of 6
  months, a member will have paid 37 to the club.
  At the end of 10 months, 45 will have been paid.
  What are the monthly dues and initiation charge?

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