PreCalculus
Chapter 10 Test
Name
Directions: Show all work and reasoning to receive full credit.
1
The Lincoln Center charges $21 for adults, $15 for senior citizens and $10 for children under 12 for
their holiday spectacular concert. The paid revenue for the show was $13,167 for 874 tickets sold.
There were 48 more children than adults. How many children attended the show?
2
Write the following system of equations in an augmented matrix and solve the system by using GaussJordan elimination to get the augmented matrix in reduced row echelon form.
2 x  9 y  z  78

 x  8 y  8 z  93
8 x  y  z  36

3
Solve the system of equations using the inverse method.
2 x  4 y  5 z  8

 x  5 y  2 z  1
3x  3 y  3z  15

4
Use Cramer’s Rule to solve the system of equations.
6 x  7 y  4 z  50

6 x  4 y  8 z  62
5 x  4 y  7 z  66

5.
Write the partial fraction decomposition of the rational expression.
4x
2
2 x  3x  2
6.
Write the partial fraction decomposition of the rational expression.
x2  9
x4  2 x2  8
7.
Graph the region and find the maximum value of the objective function z  9 x  6 y subject to the
constraints:
4
x0
y0
3
x y 3
2 x  5 y  10
2
x y 1
1
-1
1
2
3
-1
8.
A sports drink company has two popular flavors, citrus and orange. Besides water, each contains two
important ingredients, potassium and sodium. Orange contains 5 grams of potassium per gallon and 2
grams of sodium per gallon. Citrus contains 3 grams of potassium per gallon and 6 grams of sodium per
gallon. The company has 360 grams of potassium and 480 grams of sodium available for production per
hour. Each gallon of orange produces a profit of $2 and each gallon of citrus produces a profit of $2.50.
Write an objective function and constraints. Find the number of each to produce maximum profit.
4