1. Real-world applications of linear equations in three variables Unit 1 Day 13

2. A-REI. 6: I can solve systems of linear equations exactly. A-REI
A-REI.6: I can solve systems of linear equations exactly. A-REI.11: I know the point of intersection of multiple graphs is the solution to the equations. I can find the intersection point of a function using various methods. A-CED.1: I can solve a real-world problem by writing and solving an appropriate linear equation.

3. When solving problems involving three variables, use the four-step plan to help organize the information.
Identify the three variables and define what they represent.
Use the information from the word problem to form equations using the variables.
Solve the problem.
Answer the question that was provided in the word problem.

4. Seats in front section of the amphitheater stage cost $30
Seats in front section of the amphitheater stage cost $30. The seats in the middle section cost $25, and the lawn seats cost $20. There are twice as many seats in the middle section as in the front section. When all 19,200 seats are sold out, the amphitheater makes $456,000. Determine how many seats are in each section of the amphitheater.

5. f=number of seats in the front section of the amphitheater
f=number of seats in the front section of the amphitheater. m=number of seats in the middle section of the amphitheater. l=number of seats in the lawn section of the amphitheater.

7. Ex.1 Application
STEP 3: Use the equation that was not chosen in Step 1 and pair it with one of the other original equations to eliminate the y variable
STEP 1: Identify two equations and a variable to eliminate
New Equation 2
STEP 2: Eliminate one of the variables in two of the original equations
New Equation 1

8. STEP 4: Solve the NEW system of equations using New Equation 1 and New Equation 2
STEP 5: Substitute the value from Step 4 into the either New Equation 1 or New Equation 2 and solve for x.
STEP 6: Substitute you’re the values from Step 4 and Step 5 into any of the three original equations and solve for y.

9. There are 3,600 seats in the front section of the amphitheater, 7,200 seats in the middle section and 8,400 lawn seats.

10. Diana goes to the amusement park to ride the roller coaster, bumper cars and water rides. The wait for the roller coaster is 1 hour, the wait for the bumper cars is 20 minutes long, and the wait for the water rides is just 15 minutes long. Diana rode ten total rides during her visit to the amusement park. Because she enjoys roller coasters the most, the number of times she rode the roller coaster was the sum of the times she rode the other two rides. If Diana waited in line a total of 6 hours and 20 minutes, how many of each ride did she go on?

11. r=number of times she rode the roller coaster
r=number of times she rode the roller coaster. b=number of times she rode the bumper cars. w=number of times she went on the water ride.

13. Ex.2 Application
STEP 3: Use the equation that was not chosen in Step 1 and pair it with one of the other original equations to eliminate the y variable
STEP 1: Identify two equations and a variable to eliminate
New Equation 2
STEP 5: Substitute the value from Step 4 into the either New Equation 1 or New Equation 2 and solve for x.
STEP 2: Eliminate one of the variables in two of the original equations
New Equation 1
STEP 6: Substitute you’re the values from Step 4 and Step 5 into any of the three original equations and solve for y.

14. Diana rode the roller coaster five times, bumper cars one and the water ride four times.