Systems of Equations - Word Problems

Systems of Equations - Word Problems

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I. School Dance

 Mrs. Glynn and the student council planned the Homecoming Dance. They took in $3,000 to pay for the DJ, decorations, police detail and other expenses. Tickets cost $15 or $10 with a can good donation. 250 students bought tickets to the dance. How many tickets of each type were sold?

Open Ended

In your own words, what is this question asking you to find?

Step 1

Identify the variables

Multiple Choice

For the school dance, what should the variables represent?

• x = number of people who bought $15 tickets

  y = number of people who bought $10 tickets

• x = cost of the DJ

  y = cost of the decorations

  z = the cost of the police detail

• x = Total cost spent

  y = Total number of people

Step 2

Determine what your equations should represent. (Hint: For this example, there will be two equations.)

Multiple Select

Determine what should your two equations represent. Choose TWO.

• Total number of tickets purchased.

• Total earned from ticket sales.

• Total of all the expenses

• Total number of students in the Student Council

• Total level of Mrs. Glynn's awesomeness

Step 3

Create your (two) equations.

Multiple Choice

Which equation represents the total number of tickets purchased.

• $$x+y=250$$

• $$15x\ +\ 10y\ =\ 3000$$

• $$250\ +\ 15x\ =\ 3000\ +10y$$

• $$15x\ +\ 10y\ =250$$

• $$x+y=3000$$

Multiple Choice

Which equation represents the total earned from ticket sales.

• $$x+y=250$$

• $$15x\ +\ 10y\ =\ 3000$$

• $$250\ +\ 15x\ =\ 3000\ +10y$$

• $$15x\ +\ 10y\ =250$$

• $$x+y=3000$$

Multiple Choice

Now which represents your SYSTEM OF EQUATIONS?

• 
  

  $$x+y\ =250$$
  

  
  $$15x\ +\ 10y\ =\ 3000$$
  

• $$x+y=3000$$
  $$15x+10y=250$$
  

• $$x+y=250$$ $$x+y=3000$$

• $$15x+10y=250$$
  
  $$15x+10y=3000$$
  

Step 4

Determine which method you will use to solve the system of equations.

Poll

Which method do you think is the best way to solve this system of equation?

• Graphing

• Substitution

• Elimination

Step 5

Solve the system.

Fill in the Blank

Now solve the system of equations.

$$x+y=250$$  

$$15x+10y=3000$$  

Please write your answer as an ordered pair,  $$\left(x,\ y\right)$$  .

Step 6

Make sure your answer makes sense.

Open Ended

$$x=100$$ , what does that represent?

Open Ended

$$y=150$$ , what does that represent?

Open Ended

What questions do you have?

Fill in the Blank

The students at Plymouth South and the students at Plymouth North both planned trips to Six Flags. The students at South rented and filled 2 vans and 11 buses with 674 students. North rented and filled 6 vans and 14 buses with 882 students. Each van and each bus carried the same number of students.

Find the number of students in each van and in each bus. (Write your answer as an ordered pair.)

Fill in the Blank

The senior classes at Plymouth North and Silver Lake planned separate trips to the indoor climbing gym. The senior class at North rented and filled 13 vans and 3 buses with 176 students. Silver Lake rented and filled 4 vans and 2 buses with 80 students. Every van had the same number of students in it as did the buses.

Find the number of students in each van and in each bus. (Write your answer as an ordered pair.)

Open Ended

What questions do you have?