Download Name - Garnet Valley School District

Warm Up – Similar to last problem in yesterday’s class work
Sue Flay and Cassa Roll obtain a franchise to operate a hamburger stand for a well-known national hamburger
chain. They pay $20,000 for the franchise, and have additional expenses of $250 per thousand hamburgers they
sell. They sell the hamburgers for $.75 each, so they take in revenue of $750 per thousand burgers.
a. Let r(x) be the number of dollars revenue they take in by selling x thousand burgers. Write the
particular equation for function r.
b. Calculate the revenue for selling 20,000, 50,000 and zero burgers.
c. Let c(x) be the total cost of owning the hamburger stand, including the $20,000 franchise fee. Write the
particular equation for function c.
d. Calculate the cost for selling 20,000, 50,000 and zero burgers.
e. How many hamburgers must Sue and Cassa sell in order to break even?
Algebra III
Systems of Equations
*Plot points and graphing lines in three dimensions
*Solving a 3 x 3 determinant and revisiting systems of 3 equations
Coordinate Plane
Plot (5, 2, 2) and (5, 2, 0)
 Cannot make a meaningful 3-D graph in a 2-D coordinate plane
 Another alternative is finding an xy-trace, a yz-trace and an xz-trace, plotting points and graphing the
PLANE.
Example #1: Graph 2x +3y +4z = 12
Finding Traces
Finding Intercepts
1. xy trace:
x – intercept:
2. xz trace:
y – intercept:
3. yz trace:
z – intercept:
Example #2
Graph 6x – 4y – 3z = 24
Graph
Algebra III
Systems of Equations
Solve a 3 X 3 Determinant
Example #1
Step 1:
4
1
0
-2
-2
7
Step 2:
2
3
5
Step 3:
Step 4:
Example #2
2
-1
3
3
5
-1
-1
3
-6
Solve the system using determinants.
3x – y + z = 2
5x + 2y – 3z = 1
2x – 3y + 4z = 3
Homework: Worksheet
Algebra III
Systems of Equations
1. A financial planner wants to invest $8,000. He wants to put some in stocks earning 15% annually and
the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of $930
annually from the two investments?
2. Tickets to a local movie were sold at $6 for adults and $4.50 for students. If 510 tickets were sold for a
total of $2580, how many adult tickets were sold?
3. Solve the system:
2x + 3y – z = -1
-x + 5y +3z = -10
3x – y – 6z = 5
p. 137, 1 b – e and page 141, 3, 4