Project #5024 - Solving and graphing word problem

  Problem Statement


Jennifer must find appropriate Day Care for her one year old child in order to take a new job working as an Executive Assistant for Taylor Publishing.  Her new job requires her to work Monday through Friday from 9:00 Am to 5:00 with the following exceptions:


·         On Monday she is scheduled to work from 10:00 AM to 5:00 PM due to additional time she is required to work later in the week


·         On Wednesday she will drop her child off one half hour early to attend an exercise class


·         On Thursday she is required to be in the Office one hour early for a staff meeting that she must be available to take notes


·         On Friday’s she attends a class at a local Community College from 5:30 to 7:00 PM and cannot pick up her child until 7:30 PM


Jennifer has carefully visited and interviewed several different Day Care operators and has decided between two of the best that she has rated for convenience, distance from work and home, safe environment for her child and ratings provided by the local County which keeps records on Day Care centers in her local community.


Jennifer lives and works in close proximity to both of the providers.  Her travel time from home, Day Care and Office is within 20 minutes travel time and therefore has allotted 30 minutes for drop off and pick up in analyzing time and cost associated Day Care charges. Jennifer is now ready to prepare some analysis to help with her decision in choosing the Day Care that will be most economical for her situation. 




Option 1 – Home based Day Care


Option 1 detail:


·         Operating hours are 7:00 AM to 8:00 PM


·         Rate hourly - $8.00 per hour


·         The Day Care does not operate on weekends or holidays


 Option 2 – Happy Time Day Care


Option 2 detail:


·         Operating hours are 7:00 AM to 8:00 PM


·         Rate is weekly $300.00 with the following pricing formula


o   Weekly rate is pro-rated at $60.00 per day


o   Day is considered to be 8 hours of service


o   A premium is charged for any additional hours over 8 per day at a rate of $10.00 per hour


o   The Day Care does not operate on holidays or weekends


Must complete the following:

  1. Analyze the cost of each option algebraically by doing the following:

           -Develop an algebraic equations(s) with clearly defined variables to to represent the cost of each option (note a single option may require 2 equations)

  1. Explain the reasoning process used to translate the written description of each cost option into algebraic expressions
  2. Solve the system of equations algebraically to determine where the two cost options are equivalent showing all work
  3. Explain each step used to solve the system of equations and include the following:

         -all mathematical operations used to solve the system of equations

         -solution(s) of the system of equations in ordered pair notation

  1. Depict the problem on a single graph (using an excel spreadsheet application) and do the following:

         -label each axis of the coordinate plane with descriptive labels

         -label all graphical solutions of the sytem of equations as "solution" and include the ordered pair

          -In a legend indicate which cost option corresponds with each line


Work needs to include all details iand seperartley an excel file must be sent with the graphical spreadsheet solution



Subject Mathematics
Due By (Pacific Time) 27
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