1
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
TASK 2.12.2: SUSIE’S HOMEWORK
Solutions
For her mathematics class, Susie was given the assignment of examining the following
scenario.
Nowhere High School is having a fund raiser. The school decided to host a donkey
basketball game with the teachers vs. the local policemen and firemen. The rules of the
game are simple. Each team will be assigned 5 donkeys. These donkeys become
extensions of the players. Each player is given a donkey and cannot let go of its reins
while they are on the court. You can get off the donkey to catch the ball but the only
time a shot counts is when the shooter is actually riding the donkey. Fun, fun! The
trouble is that the fundraising committee does not know how much to charge for tickets.
The committee realizes that they need different prices for adults and students. Their only
restriction is that a family of four (2 adults and 2 students) must be able to attend the
game for $15.00. The committee has narrowed the choices to the following three
options.
Option 1:
Adult ticket $5.00
Student ticket $2.50
Option 2:
Adult ticket $4.50
Student ticket $3.00
Option 3:
Adult ticket $5.50
Student ticket $2.00
On the day the assignment was due, Susie presented the following graphs. She said that
she had done some other stuff but unfortunately she discovered this morning that her dog
Harry had eaten everything but the piece of paper containing the following two graphs.
We must decide if Susie deserves any credit for her work.
Graph I
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
2
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
1. What is the function rule for Susie’s Graph I? What are the domain and range?
y= -4/11 x + 400; The domain appears to be 0 to 1100 and the range, 0 to 400. Given
the situation though, if this graph is to correspond to one of our options, the domain
can only be the integers between 0 and 1100 and the range, the corresponding
integers that result. Note that the graph of the situation would be a scatter plot;
however, the graph of the function rule is a line.
2. Does the graph represent one of the options? If so, which one? If not, how do you
know? If the graph represents one of the options, what is the dependent variable? The
independent variable? Why? Option 3. There are many different ways of
determining this and the instructor must carefully determine the correctness of the
individual responses. One method is to note that the slope of the graph is ! 114 . In our
situation, this means that 114 is the ratio of the price of the student ticket to the price of
the adult ticket. Option 3 is the only option that reflects this ratio. Thus the dependent
variable is the number of adults tickets sold; the independent variable is the number
of student tickets sold.
3. What is the slope of the line? What does the slope mean in this situation?
The slope is -4/11. This means that for every increase of 11 student tickets sold, the
number of adult tickets sold decreases by 4.
4. What is the y-intercept of the line? What does this point mean in this situation? The
y-intercept is (0, 400). This represents that if no student tickets are sold, 400 adult
tickets will be sold.
5. What is the x-intercept of the line? What does this point mean in this situation? The
x-intercept is (1100, 0). This represents that if 1100 student tickets are sold, no adult
tickets will be sold.
6. Using the graph, explain how can you determine how much money was earned from
the donkey basketball game. This can be easily determined using either the yintercept or the x-intercept or any other point on the line. Let’s use the y-intercept, (0,
400). Substituting these values into option 3, we get 5.5(400)+2(0)=$2,200.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
3
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
Graph II
7. What is the function rule for Susie’s Graph II? What are the domain and range?
y= -1/5 x + 352; The domain is 0 to 1760 and the range, 0 to 352. Given the
situation, if this graph is to correspond to one of our options, the domain can only be
the integers between 0 and 1760 and the range, the corresponding integers that result.
8. Does Graph II represent one of the options? Why or why not? If not, develop a new
option that this graph would represent. Explain what details of Graph II helped you
to develop your new option. This graph does not represent any of the options that the
committee was examining. The slope of the line of Graph II is m=-1/5. Thus we can
use the fact that 1/5 also represents the ratio of the student ticket price to the adult
ticket price to help us determine the option that fits the graph. We also know that all
options must allow for 2 adults and 2 students to attend the game for $15. Letting A
represent the cost of an adult ticket and S be the cost of a student ticket, we have
2A+2S=15 and SA = 15 . Solving these equations simultaneously shows that A=$6.25
and S=$1.25.
9. How is the line in Graph I related to the line in Graph II? Both graphs model
combinations of adult tickets and student tickets that result in earnings of $2,200.
10. Does Susie deserve credit for her graph? Why or why not? Susie’s Graph I does
match one of the options. Susie’s Graph II does not match one of the options but is
an example of a new option that also shows the number of adult and student tickets
that will result in an earning of $2,200. It does appear that Susie was working on the
problem so she does deserve a little credit.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
4
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
TASK 2.12.2: SUSIE’S HOMEWORK
For her mathematics class, Susie was given the assignment of examining the following
scenario.
Nowhere High School is having a fund raiser. The school decided to host a donkey
basketball game with the teachers vs. the local policemen and firemen. The rules of the
game are simple. Each team will be assigned 5 donkeys. These donkeys become
extensions of the players. Each player is given a donkey and cannot let go of its reins
while they are on the court. You can get off the donkey to catch the ball but the only
time a shot counts is when the shooter is actually riding the donkey. Fun, fun! The
trouble is that the fundraising committee does not know how much to charge for tickets.
The committee realizes that they need different prices for adults and students. Their only
restriction is that a family of four (2 adults and 2 students) must be able to attend the
game for $15.00. The committee has narrowed the choices to the following three
options.
Option 1:
Adult ticket $5.00
Student ticket $2.50
Option 2:
Adult ticket $4.50
Student ticket $3.00
Option 3:
Adult ticket $5.50
Student ticket $2.00
On the day the assignment was due, Susie presented the following graphs. She said that
she had done some other stuff but unfortunately she discovered this morning that her dog
Harry had eaten everything but the piece of paper containing the following graphs. We
must decide if Susie deserves any credit for her work.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
5
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
Graph I
1. What is the function rule for Susie’s Graph I? What are the domain and range?
2. Does the graph represent one of the options? If so, which one? If not, how do you
know? If the graph represents one of the options, what is the dependent variable? The
independent variable? Why?
3. What is the slope of the line? What does the slope mean in this situation?
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
6
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
4. What is the y-intercept of the line? What does this point mean in this situation?
5. What is the x-intercept of the line? What does this point mean in this situation?
6. Using the graph, explain how can you determine how much money was earned from
the donkey basketball game.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
7
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Task 2.12.2
Graph II
7. What is the function rule for Susie’s Graph II? What are the domain and range?
8. Does Graph II represent one of the options? Why or why not? If not, develop a new
option that this graph would represent. Explain what details of Graph II helped you
to develop your new option.
9. How is the line in Graph I related to the line in Graph II?
10. Does Susie deserve credit for her graph? Why or why not?
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.