USING SYSTEMS OF LINEAR EQUATIONS TO SOLVE REAL WORLD PROBLEMS ASSIGNMENT #:______
(FCAT: THINK, SOLVE AND EXPLAIN)
R. CARRASCO
NAME:_____________________________DATE:___________PER:_____
In problems 1 and 2, a) set up a system of linear equations and b) solve the problem.
Answer the problems in full sentences.
1)a)
1) Twice a number added to five times another number equals two.
The first number is equal to negative three times the second number.
b)
2) Three times a number minus five times another number equals
seventeen. The first number is equal to negative four times the
second number.
2)a)
b)
Use the following information for problems 3 through 7:
At Mark’s gym you can have two plans for becoming a member:
PLAN A: Pay $400 per year.
PLAN B: Pay $100 per year plus $50 per week.
3)
4)
3) Determine a system of equations.
4) Graph the system. Label the axes according to the problem.
5) Find the break-even point using the graph and check algebraically.
(Solve the system algebraically here)
5)
6) Explain the meaning of the break-even point.
7) a) Based on the break-even point, If Mary plans to visit the gym
exactly 8 weeks, which plan would be the most economical?
b)
What would be her cost for the 8 weeks?
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7)a)
b)
c)
If the gym decides to eliminate Plan A, how many weeks will she be allowed to visit the
gym if she pays $850?
USING SYSTEMS OF LINEAR EQUATIONS TO SOLVE REAL WORLD PROBLEMS
- PAGE 2 - (FCAT: THINK, SOLVE AND EXPLAIN) R. CARRASCO
Use the following information for problems 8 and 9:
A school club is selling 2 types of candy (“Crunchy” and “Buttery”) as a
fund raiser. Crunchy sells for $2.00 a piece, and Buttery sells for $3.00 a
piece. The club sold a combined total of 205 pieces of candy for a total
amount of $565.
8) Write a system of linear equations for this problem.
8)
9) Solve the system by any method and state how many pieces of each
candy were sold.
9)
# pieces of Crunchy:_________
# pieces of Buttery:_________
10)
11)
Use the following information for problems 10 through 14:
The Math Club is planning a T-shirt sale. The T-shirt company charges
$78 for the setup fee and $4 for each printed shirt. The Math Club is
planning to sell each T-shirt for $10.
10) Write a system of linear equations for this problem.
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13)
11) Find the break-even point by any method.
14)
12) Explain the meaning of the break-even point. Include in your explanation the meaning of
before and after the break-even point.
13) How much profit will the Math Club make if it sells 100 T-shirts?
14) How much profit will the Math Club make if it purchases 100 shirts from the manufacturer but
sells only 75?