Suppose you are the student council members and are responsible for
planning the Winter Formal. Plans include hiring a DJ, buying decorations, and
buying and serving dinner. You already have a location donated for the event.
You want to keep the ticket prices as low as possible to encourage as many
students to attend.
As you work through the following sections, you will use systems of equations to analyze costs and make
decisions. In the end, you will write a summary detailing your choice of DJ and decorations, the cost of
the catering service and your ticket price recommendation.
Section 1: The DJ
DJ Jazzy Jeff charges $2000 for the evening. DJ Fresh Prince just charges $5 for each ticket sold. Define
your variables and write a system of equations to represent the situation. Graph the system on graph
paper and find the number of tickets for which the cost of the two DJs would be equal.
Section 2: the caterer
A caterer charges a fixed cost for preparing a dinner, plus an additional cost for each person served. You
know that the cost for 200 students will be $1500 and the cost for 300 students will be $2100. Define
your variables and write a system of equations to represent the situation. Solve the system using
elimination and determine the caterer’s fixed cost and the cost per student served.
Section 3: Decorations
A designer will be hired to take care of the decorations. Downtown Designs charges a fixed cost of $200
plus $50 per table decoration. ABC Designs charges a fixed cost of $350 plus $40 per table decoration.
Define your variables and write a system of equations to represent the situation. Solve the system
using substitution and find the number of tables for which the costs would be equal.
Section 4: Analysis
Use the information from Sections 1, 2 & 3 to complete the following:
Assume that 200 students attend the prom for which you will use 10 tables. Write a summary
listing which DJ and decorator you would choose and the cost per ticket you would need to
charge to cover expenses. Show all justifications.
Assume that 600 students attend the prom and you will use 18 tables and repeat the process.
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