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Here are some examples of systems to be solved.  Please show your work and explain how you develop the equations.

a)    Mike runs twice as far as Jim, but Phillip runs three times as far as Jim.  If the three of them run a total of 24 miles, how far does each man run?

b)    PurePets dog food is 65% vegetables 35% meat and grain.  NewTone dog food is 42% vegetables and 58% meat and grain.  How much of each would be  

       needed to produce 25 pounds of dog food that was 50% vegetable and 50% meat and grain?






You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an $80,000 loan from your family and a $38,250 small business loan. These loans must be repaid in full within 10 years.


  1. What integer would represent your total budget?
  2. Twenty-five percent of your budget will be used to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve.
  3. How much money will rent and utilities cost? Explain how you arrived at this answer.