1. Section 8.3 Problems Involving Linear and Quadratic Systems
Pre-Calculus 11
Chapter 8.2 Continued

2. I) Review:

3. II) Solving Problems Involving Linear Systems
Applications: Investments, Science in sports
Indicate What the Variables are
Number of People
Cost for a certain item
Read the Question to generate your 2 equations
Quantity
Revenue
Solve the system by Elimination or Substitution

4. Example: A tutoring center charges an annual fee and an hourly fee
Example: A tutoring center charges an annual fee and an hourly fee. 8 hours of tutoring cost $ hours cost $500. Find the annual cost and hourly cost.
Let “x” be the Annual Cost
Let “y” be the Hourly Cost
Indicate the Variables
Make the Equations
Solve by Elimination
The Hourly cost is $30 per hour
The Annual cost is $50 per year

5. Practice: The cost for a school play is $35 per adult and $20 per student. 160 people attended the play and total revenue was $ How many students and adults attended?
Indicate the Variables
Let “x” be the Number of Adults
Let “y” be the Number of Students
Make the Equations
Quantity
Revenue
Solve by Elimination
100 students and 60 parents attended the school play

6. Example: James invested $9000, part with Bank A (3%) and part with Bank B (5%). After one year, he made a total of $340 in interest. How much did he invest with each bank?
Total Investment $9000
Indicate the Variables
Let “A” be amount invested in Bank A
Amount $A
Bank A (3%)
Amount $B Bank B (5%)
Let “B” be amount invested in Bank B
James invested $5500 with Bank A and $3500 with Bank B
Make the Equations
Solve by Elimination

7. James invested $3500 with Bank A and $6500 with Bank B
Example: James invested $10000, part with Bank A (7%) and part with Bank B (13%). After one year, both banks made the same amount of Interest. How much did he invest with each bank?
Indicate the Variables
Total Investment $10000
Let “A” be amount invested in Bank A
Amount $A
Bank A (7%)
Amount $B Bank B (13%)
Let “B” be amount invested in Bank B
Make the Equations
Solve by Substitution
James invested $3500 with Bank A and $6500 with Bank B

8. Ex: In basketball, the arc of a shot can be simulated by a parabola [quadratic function].

10. Ex: Using the Noah system, a perfect foul shot made by a 6ft tall player has a quadratic equation of: In order for the ball to enter the basket at 45 degrees, the slope at the point (15,10) should be -1. Find the values of “a” and “b”
Use the coordinates to simplify the equation: x=15, y=10

11. Solve by Elimination
Solve for “b”
So the perfect foul shot by a 6ft tall player would be:

12. A nuclear was misfired near the east coast and is on a trajectory given by the quadratic equation below. To avoid an international disaster, a second interceptor launch is to be fired to detonate the first one. The trajectory of the second launch is given below. Calculate at what point the two will collide.
Canada

13. The missile will detonate the nuclear bomb at 13,964km away at a height of 3585.672km
Extraneous

14. Challenge: A musical charges $4. 00 for adults and $2. 50 for children
Challenge: A musical charges $4.00 for adults and $2.50 for children. On the first night, the ratio of adults to kids was 3:5. On the second night, the ratio was 2:3. A total of 1390 people attended for two nights, and the revenue generated was $ How many adults and kids attended?
Adults $4.00
Kids $2.50
Total Attendance 3x
1st Night 5x 8x
2nd Night 2y 3y 9y
Revenue
4 x (3x+2y)
2.5 x(5x+3y)

15. Challenge: A musical charges $4. 00 for adults and $2. 50 for children
Challenge: A musical charges $4.00 for adults and $2.50 for children. On the first night, the ratio of adults to kids was 3:5. On the second night, the ratio was 2:3. A total of 1390 people attended for two nights, and the revenue generated was $ How many adults and kids attended?
Make the Equations
Quantity
Revenue

16. Challenge: A musical charges $4. 00 for adults and $2. 50 for children
Challenge: A musical charges $4.00 for adults and $2.50 for children. On the first night, the ratio of adults to kids was 3:5. On the second night, the ratio was 2:3. A total of 1390 people attended for two nights, and the revenue generated was $ How many adults and kids attended?
Adults $4.00
Kids $2.50
Total Attendance
3(80)
5(80)
1st Night
=240
=400
2(150)
3(150)
2nd Night
=300
=450
Total Attended
=540 adults
=850 kids

17. Homework: