Deck 4: Systems of Equations and Inequalities

Question 1

Determine whether the ordered pair is a solution of the system of linear equations
$( 1 , - 3 ) , \left\{ \begin{array} { l } 2 x + y = - 1 \\4 x + 2 y = - 2\end{array} \right.$

A) Yes
B) No

Answer 1

A

Question 2

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.$$

A) $( - 7 , - 1 )$
B) $( 7,0 )$
C) $( 8,7 )$
D) $\varnothing$

Answer 2

B

Question 3

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.$$

A) $( - 5,12 )$
B) $( 8 , - 12 )$
C) $( 6 , - 12 )$
D) $\varnothing$

Answer 3

A

Question 4

A) $( 1,3 )$
В) $\left( \frac { 1 } { 2 } , 0 \right)$
C) $\left( \frac { 3 } { 2 } , 0 \right)$
D) $\varnothing$

Question 5

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { r } x + 8 y = 35 \\7 x + 7 y = 0\end{array} \right.$$

A) $( 5,6 )$
В) $( - 5,5 )$
C) $( - 6,6 )$
D) $\varnothing$

Question 6

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { r } x - 5 y = - 7 \\- 7 x - 5 y = - 71\end{array} \right.$$

A) $( - 3,8 )$
B) $( 8,3 )$
C) $( 3,8 )$
D) $\varnothing$

Question 7

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.$$

A) $( - 1 , - 3 )$
В) $( 1 , - 3 )$
C) $( - 1,3 )$
D) $( 1,3 )$

Question 8

A) $( - 1 , - 6 )$
B) $( 1,12 )$
C) $( - 1,6 )$
D) $( 1 , - 6 )$

Question 9

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.$

A) Yes
B) No

Question 10

Solve the system of equations by the substitution method.
$$\left\{ \begin{aligned}3 x - 4 y & = 32 \\x & = - 4 y\end{aligned} \right.$$

A) $( - 8 , - 2 )$
В) $( - 2,8 )$
C) $( 8,2 )$
D) $( 8 , - 2 )$

Question 11

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { r } x + 7 y = 35 \\- 4 x + 8 y = 40\end{array} \right.$$

A) $( 1,4 )$
B) $( 0,5 )$
C) $( - 5,0 )$
D) $\varnothing$

Question 12

Determine whether the ordered pair is a solution of the system of linear equations
$( 4,3 ) , \left\{ \begin{array} { l } 4 x + y = 13 \\3 x + 4 y = 0\end{array} \right.$

A) Yes
B) No

Question 13

Solve the system by graphing.

A) (-4, -1)
B) (0, -1)
C) (0, -4)
D) $\phi$

Question 14

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { l } 8 x - 5 y = 69 \\2 x + y = 15\end{array} \right.$$

A) $( 7,0 )$
B) $( 8 , - 1 )$
C) $( 8,0 )$
D) $\varnothing$

Question 15

Determine whether the ordered pair is a solution of the system of linear equations
$( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.$

A) Yes
B) No

Question 16

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.$$

A) $( 2 , - 4 )$
B) $( - 2,4 )$
C) $( - 2 , - 4 )$
D) $( 2,4 )$

Question 17

Determine whether the ordered pair is a solution of the system of linear equations
$( 3,3 ) , \left\{ \begin{array} { l } x + y = 0 \\x - y = - 6\end{array} \right.$

A) Yes
B) No

Question 18

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { r } x - 5 y = - 10 \\2 x - 6 y = - 8\end{array} \right.$$

A) $( 4,4 )$
B) $( 5,3 )$
C) $( - 5,4 )$
D) $\varnothing$

Question 19

Solve the system of equations by the substitution method.
$$\left\{ \begin{array} { l } \frac { x } { 7 } - \frac { y } { 8 } = 1 \\\frac { x } { 9 } - y = 8\end{array} \right.$$

A) $( - 8,0 )$
B) $( 0,8 )$
C) $( 8,0 )$
D) $( 0 , - 8 )$

Question 20

Determine whether the ordered pair is a solution of the system of linear equations
$( - 1 , - 3 ) , \left\{ \begin{array} { l } 2 \mathrm { x } = - 1 - \mathrm { y } \\3 \mathrm { x } = - 3 - 2 \mathrm { y }\end{array} \right.$

A) Yes
B) No

Question 21

Solve the system of equations.
$$\left\{ \begin{array} { l } \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \\\frac { x } { 4 } = \frac { 2 y + 6 } { 8 }\end{array} \right.$$

A) $( - 1,2 )$
B) $( 2 , - 1 )$
C) $\left\{ ( x , y ) \mid \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \right\}$
D) $\varnothing$

Question 22

Solve the system of equations.
$$\left\{ \begin{aligned}y & = - 3 x \\- 3 x + y & = - 6\end{aligned} \right.$$

A) $( - 1,3 )$
B) $( 1,6 )$
C) $( 1 , - 3 )$
D) $\varnothing$

Question 23

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { l } 4 x + y = 19 \\3 x + 4 y = - 2\end{array} \right.$$

A) $( - 5,6 )$
B) $( 6 , - 5 )$
C) $( 0 , - 5 )$
D) $\varnothing$

Question 24

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { l } 7 x + 4 y = - 1 \\2 x + 3 y = - 2\end{array} \right.$$

A) $\left( - \frac { 12 } { 13 } , \frac { 5 } { 13 } \right)$
В) $\left( \frac { 5 } { 13 } , \frac { 12 } { 13 } \right)$
C) $\left( \frac { 5 } { 13 } , - \frac { 12 } { 13 } \right)$
D) $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$

Question 25

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { r } 2 x + 10 y = - 48 \\12 x + 2 y = 60\end{array} \right.$$

A) $( 6 , - 6 )$
В) $( 12 , - 12 )$
C) $( - 6,6 )$
D) $( - 2,6 )$

Question 26

Solve the system of equations.
$$\left\{ \begin{aligned}5 x + 3 y & = - 7 \\x & = - 2 y\end{aligned} \right.$$
B) $( - 2,1 )$

A) $( 1 , - 2 )$
C) $\{ ( x , y ) \mid 5 x + 3 y = - 7 \}$
D) $\varnothing$

Question 27

Solve the system of equations.
$$\left\{ \begin{array} { l } y = 3 x + 2 \\y = 8 x + 1\end{array} \right.$$

A) $\left( \frac { 1 } { 5 } , \frac { 13 } { 5 } \right)$
B) $\left( \frac { 13 } { 5 } , \frac { 1 } { 5 } \right)$
C) $\{ ( x , y ) \mid y = 3 x + 2 \}$
D) $\varnothing$

Question 28

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
If the company sells 3000 bottles of mouthwash, does the company make money or lose money?

Question 29

Solve the system of equations.
$$\left\{ \begin{array} { r } \frac { 3 } { 10 } x + \frac { 1 } { 2 } y = \frac { 47 } { 10 } \\3 x + 2 y = 53\end{array} \right.$$

A) $( 19 , - 2 )$
B) $( - 19,3 )$
C) $( - 2,19 )$
D) $( - 19,5 )$

Question 30

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
Find the coordinates of the point of intersection, or breakeven point, by solving the system
$$\left\{ \begin{array} { l } y = 1.3 x \\y = 0.5 x + 2500\end{array} \right.$$
and explain its meaning.

Question 31

Solve the system of equations.
$$\left\{ \begin{array} { l } \frac { x } { 3 } + \frac { y } { 9 } = 1 \\\frac { x } { 2 } - \frac { y } { 6 } = 0\end{array} \right.$$

A) $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$
B) $\left( \frac { 9 } { 2 } , \frac { 3 } { 2 } \right)$
C) $\left\{ ( x , y ) \mid \frac { x } { 3 } + \frac { y } { 9 } = 1 \right\}$
D) $\varnothing$

Question 32

Solve the system of equations.
$$\left\{ \begin{aligned}y & = 4 x + 5 \\4 y + 12 x & = 132\end{aligned} \right.$$

A) $( 4,21 )$
В) $( 21,4 )$
C) $\{ ( x , y ) \mid y = 4 x + 5 \}$
D) $\varnothing$

Question 33

Solve the system of equations by the elimination method.
$$\left\{ \begin{aligned}7 x + y & = 3 \\3 y & = 9 - 21 x\end{aligned} \right.$$

A) $\left( \frac { 3 } { 7 } , 0 \right)$
B) $( 0,3 )$
C) $\{ ( x , y ) \mid 7 x + y = 3 \}$
D) $\varnothing$

Question 34

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { r } - x - 2 y = - 8 \\- 9 x - 18 y = 2\end{array} \right.$$
B) $( 0,4 )$

A) $( 8,0 )$
D) $\varnothing$
C) $\{ ( x , y ) \mid - x - 2 y = - 8 \}$

Question 35

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
If the company sells 3500 bottles of mouthwash, does the company make money or lose money?

Question 36

Solve the system of equations.
$$\left\{ \begin{aligned}3 y & = x + 18 \\3 x + 9 y & = 0\end{aligned} \right.$$

A) $( 3 , - 9 )$
В) $( - 9,3 )$
C) $\{ ( x , y ) \mid 3 y = x + 18 \}$
D) $\varnothing$

Question 37

Solve the system of equations by the elimination method.
$$\left\{ \begin{array} { l } - 3 x - 7 y = - 26 \\- 5 x + 4 y = 35\end{array} \right.$$

A) $( - 3,5 )$
B) $( 3 , - 5 )$
C) $( 3,5 )$
D) $( - 3 , - 5 )$

Question 38

Solve the system of equations.
$$\left\{ \begin{array} { l } 3.5 x + 0.2 y = - 10.9 \\0.7 x - 0.6 y = - 0.9\end{array} \right.$$

A) $( 0.5 , - 1.8 )$
B) $( - 3 , - 2 )$
C) $( - 6.5 , - 1.8 )$
D) $( - 3.2 , - 2 )$

Question 39

Solve the system of equations.
$$\left\{ \begin{array} { r r } 9 x - 5 y = & 4 \\- 18 x + 10 y = & - 12\end{array} \right.$$

A) $\left( \frac { 9 } { 8 } , - \frac { 5 } { 8 } \right)$
B) $( 2,3 )$
C) $\{ ( x , y ) \mid 9 x - 5 y = 4 \}$
D) $\varnothing$

Question 40

Solve the system of equations.
$$\left\{ \begin{aligned}y & = \frac { 1 } { 5 } x + 6 \\x - 5 y & = - 30\end{aligned} \right.$$

A) $( 0,6 )$
B) $( - 30,0 )$
C) $\left\{ ( x , y ) \mid y = \frac { 1 } { 5 } x + 6 \right\}$
D) $\varnothing$

Question 41

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
For what x-values will the company lose money?

Question 42

Solve the system.
$$\left\{ \begin{aligned}x + y & = - 7 \\2 x - 2 y + 3 z & = 13 \\x - z & = - 9\end{aligned} \right.$$

A) $( - 4,5 , - 3 )$
В) $( - 4 , - 3,5 )$
C) $( 5 , - 4 , - 3 )$
D) $( 5 , - 3 , - 4 )$

Question 43

Solve the system.
$$\left\{ \begin{array} { r } x - y + 4 z = - 1 \\2 x + z = 0 \\- x + y - 4 z = 2\end{array} \right.$$

A) $( 4,1,0 )$
B) $( 0,1,0 )$
C) $( 0,0,1 )$
D) $\varnothing$

Question 44

Solve.
One number is 4 less than a second number. Twice the second number is 30 more than 4 times the first. Find the two numbers.

A) $- 10$ and $- 6$
B) $- 11$ and $- 7$
C) $- 12$ and $- 8$
D) 7 and 11

Question 45

Solve the system.
$$\left\{ \begin{array} { l } x - y + z = - 11 \\x + y + z = - 1 \\x + y - z = 1\end{array} \right.$$

A) $( - 1 , - 5,5 )$
В) $( - 5,5 , - 1 )$
C) $( - 5 , - 1,5 )$
D) $\varnothing$

Question 46

Solve.
One number is 3 less than a second number. Twice the second number is 21 less than 5 times the first. Find the two numbers.

A) 9 and 12
B) $- 12$ and $- 9$
C) 10 and 13
D) 8 and 11

Question 47

Solve the system.
$$\left\{ \begin{array} { r r } x - 5 y - z = & 5 \\- 3 x + 15 y + 3 z = & - 15 \\4 x - 20 y - 4 z = & 20\end{array} \right.$$

A) $( - 3,4 , - 28 )$
B) $( 4 , - 3,14 )$
C) $\{ ( x , y , z ) \mid x - 5 y - z = 5 \}$
D) $\varnothing$

Question 48

Solve the system.
$\int 4 x + y - \frac { 2 } { 3 } z = 29$
$\left\{ \frac { 1 } { 3 } x - 2 z = 8 \right.$
$x + 2 y = 12$

A) $( - 9,4 , - 2 )$
B) $( 4 , - 3 , - 6 )$
C) $( 6,3 , - 3 )$
D) $( 4,4 , - 3 )$

Question 49

Solve the system.
$$\left\{ \begin{array} { r } x + 5 y + 2 z = 35 \\5 y + 3 z = 37 \\z = 4\end{array} \right.$$

A) $( 2,4,5 )$
B) $( 2,5,4 )$
C) $( 4,5,2 )$
D) $\varnothing$

Question 50

Solve the system.
$$\left\{ \begin{array} { l } 3 x + 3 y + z = 2 \\5 x - 5 y - z = - 16 \\4 x + y + 5 z = - 21\end{array} \right.$$

A) $( - 4,3 , - 1 )$
B) $( - 1 , - 4,3 )$
C) $( - 1,3 , - 4 )$
D) $\varnothing$

Question 51

Solve the system.
$$\left\{ \begin{array} { r r } x - y + 2 z = & - 4 \\5 x + z = 0 \\x + 2 y + z = 8\end{array} \right.$$

A) $( 0,0,4 )$
В) $( 0,4,0 )$
C) $( 0,4 , - 4 )$
D) $\varnothing$

Question 52

Solve the system.
$$\left\{ \begin{aligned}x + y + z & = 7 \\x - y + 5 z & = - 3 \\4 x + y + z & = 22\end{aligned} \right.$$

A) $( 5,3 , - 1 )$
В) $( - 1,3,5 )$
C) $( - 1,5,3 )$
D) $\varnothing$

Question 53

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
$$\left\{ \begin{array} { l } \frac { 1 } { x } + y = 20 \\\frac { 3 } { x } + y = 32\end{array} \right.$$

A) $\left( \frac { 1 } { 6 } , - 14 \right)$
В) $\left( 14 , \frac { 1 } { 6 } \right)$
C) $\left( \frac { 1 } { 6 } , 14 \right)$
D) $\left( - \frac { 1 } { 6 } , - 14 \right)$

Question 54

Solve the system.
$$\left\{ \begin{array} { r } x - y + 4 z = - 8 \\5 x + z = - 1 \\x + 4 y + z = 15\end{array} \right.$$

A) $( - 1,4,0 )$
В) $( - 1,0,4 )$
C) $( 0,4 , - 1 )$
D) $\varnothing$

Question 55

Solve the system.
$$\left\{ \begin{array} { r } x - y + 3 z = - 2 \\3 x + z = 0 \\- x + y - 3 z = 10\end{array} \right.$$

A) $( 3,2,0 )$
B) $( 0,0,2 )$
C) $( 0,2,0 )$
D) $\varnothing$

Question 56

Solve the system.
$$\left\{ \begin{aligned}x + y + z & = - 5 \\x - y + 4 z & = - 18 \\2 x + 2 y + 2 z & = - 4\end{aligned} \right.$$

A) $( 1 , - 1 , - 5 )$
В) $( - 5,1 , - 1 )$
C) $( - 5 , - 1,1 )$
D) $\varnothing$

Question 57

Solve the system.
$$\left\{ \begin{array} { r } y - 4 z = - 10 \\- 2 x + y - 5 z = - 11 \\4 x + 5 z = 11\end{array} \right.$$

A) $( 4,3 , - 1 )$
B) $( 4 , - 8 , - 1 )$
C) $( - 1,2,3 )$
D) $( - 1,6,4 )$

Question 58

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
$$\left\{ \begin{array} { l } \frac { 1 } { x } + \frac { 1 } { y } = 13 \\\frac { 1 } { x } - \frac { 1 } { y } = 1\end{array} \right.$$

A) $\left( \frac { 1 } { 6 } , \frac { 1 } { 7 } \right)$
B) $\left( \frac { 1 } { 7 } , \frac { 1 } { 6 } \right)$
C) $\left( \frac { 1 } { 13 } , 0 \right)$
D) $\varnothing$

Question 59

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.
For what x-values will the company make a profit?

Question 60

Solve the system.
$$\left\{ \begin{array} { r } x + y + z = 6 \\x - y + 3 z = 10 \\2 x + 2 y + 2 z = 8\end{array} \right.$$

A) $( 3,2,1 )$
B) $( 2,1,3 )$
C) $( 3,1,2 )$
D) $\varnothing$

Question 61

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 3 hot dogs, 3 bags of potato chips, and 3 soft drinks for $11.25. The price of a hot dog is $1.25 more than the price of a bag of potato chips.
The cost of a soft drink is $2.00 less than the price of two hot dogs. Find the cost of each item.

A) $2.00 for a hot dog; $0.75 for a bag of potato chips; $1.50 for a soft drink
B) $1.75 for a hot dog; $1.50 for a bag of potato chips; $0.50 for a soft drink
C) $0.50 for a hot dog; $1.75 for a bag of potato chips; $1.50 for a soft drink
D) $1.75 for a hot dog; $0.50 for a bag of potato chips; $1.50 for a soft drink

Question 62

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
$$\begin{array} { l } C ( x ) = 6000 x + 70,000 \\R ( x ) = 16,000 x\end{array}$$

A) 9 units
B) 3 units
C) 8 units
D) 7 units

Question 63

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
$$\begin{array} { l } C ( x ) = 11 x + 15,200 \\R ( x ) = 30 x\end{array}$$

A) 802 units
B) 800 units
C) 311 units
D) 801 units

Question 64

Solve.
University Theater sold 562 tickets for a play. Tickets cost $23 per adult and $13 per senior citizen. If total receipts were $9086, how many senior citizen tickets were sold?

A) 178 senior citizen tickets
B) 294 senior citizen tickets
C) 268 senior citizen tickets
D) 384 senior citizen tickets

Question 65

Solve.
The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $11 per pound. The manager wishes to make a 120-pound trail mix-cashew mixture that will sell for $9 per pound.
How many pounds of each should be used?

A) 100 pounds of trail mix
B) 60 pounds of trail mix 20 pounds of cashews 60 pounds of cashews
C) 80 pounds of trail mix
D) 40 pounds of trail mix 40 pounds of cashews 80 pounds of cashews

Question 66

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
$$\begin{array} { l } C ( x ) = 88 x + 2800 \\R ( x ) = 108 x\end{array}$$

A) 142 units
B) 141 units
C) 140 units
D) 22 units

Question 67

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
Find the values of $a , b$ , and c such that the equation $y = a x ^ { 2 } + b x + c$ has ordered pair solutions $( - 2 , - 6 )$ , $( 2,10 )$ , and $( 4,6 )$ .

A) $a = 1 ; b = 4 ; c = 6$
B) $a = - 1 ; b = 4 ; c = 6$
C) $a = 1 ; b = 6 ; d = 4$
D) $a = - 1 ; b = 6 ; c = 4$

Question 68

Solve.
A chemist needs 170 milliliters of a 59% solution but has only 15% and 83% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

A) 65 ml of 15%; 105 ml of 83%
B) 65 ml of 15%; 110 ml of 83%
C) 110 ml of 15%; 60 ml of 83%
D) 60 ml of 15%; 110 ml of 83%

Question 69

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
At the break-even point both cost and revenue are what?

A) $1500
B) $2700
C) $750
D) $2250

Question 70

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
$$\begin{array} { l } C ( x ) = 0.3 x + 1320 \\R ( x ) = 1.5 x\end{array}$$

A) 1120 units
B) 1110 units
C) 1100 units
D) 489 units

Question 71

Solve.
A certain aircraft can fly 1190 miles with the wind in 5 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?

A) 17 mph
B) 34 mph
C) 68 mph
D) 51 mph

Question 72

Solve.
A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 3 bags of potato chips for $9.25. Another customer buys 4 hot dogs and 5 bags of potato chips for $10.00. Find the cost of each item.

A) $1.25 for a hot dog; $1.25 for a bag of potato chips
B) $1.00 for a hot dog; $1.25 for a bag of potato chips
C) $1.50 for a hot dog; $1.25 for a bag of potato chips
D) $1.25 for a hot dog; $1.00 for a bag of potato chips

Question 73

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
A basketball player scored 16 points in a game. The number of three-point field goals the player made was 14 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals
The player made was 7 more than the number of three-point field goals made. Find the number of free-throws,
Two-point field goals, and three-point field goals that the player made in the game.

A) 6 free throws; 4 two-point field goals; 4 three-point field goals
B) 5 free throws; 4 two-point field goals; 1 three-point field goals
C) 5 free throws; 5 two-point field goals; 3 three-point field goals
D) 5 free throws; 1 two-point field goals; 4 three-point field goals

Question 74

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 4 sleeping bags, and 3 camp stools for $220. The price of the tent is 7 times the cost of a camp stool. The cost of a sleeping bag is $20 more than the
Cost of a camp stool. Find the cost of each item.

A) $77 for a tent; $30 for a sleeping bag; $11 for a camp stool
B) $70 for a tent; $35 for a sleeping bag; $15 for a camp stool
C) $70 for a tent; $30 for a sleeping bag; $10 for a camp stool
D) $70 for a tent; $30 for a sleeping bag; $11 for a camp stool

Question 75

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
Three trains  one eastbound, one westbound, and one northbound  leave a city at the same time. The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound train. After 2 hours, the
Distance between the westbound train and the eastbound train is 200 miles. Twice the speed of the westbound
Train is 100 miles per hour more than the speed of the northbound train. Find the speeds of the three trains.

A) eastbound, 40 mph; westbound, 70 mph; northbound, 30 mph
B) eastbound, 20 mph; westbound, 80 mph; northbound, 40 mph
C) eastbound, 30 mph; westbound, 70 mph; northbound, 40 mph
D) eastbound, 40 mph; westbound, 70 mph; northbound, 50 mph

Question 76

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.

A) $P ( x ) = 2 x + 1500$
B) $P ( x ) = 4 x + 1500$
C) $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } - 1500$
D) $\mathrm { P } ( \mathrm { x } ) = 4 \mathrm { x } - 1500$

Question 77

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
$$\begin{array} { l } C ( x ) = 143 x + 306,000 \\R ( x ) = 313 x\end{array}$$

A) 1801 units
B) 1800 units
C) 634 units
D) 1802 units

Question 78

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
What is the profit when 796 binoculars are produced?

A) $3092
B) $92
C) $4684
D) $1684

Question 79

Solve.
Two cars leave a city and head in the same direction. After 5 hours, the faster car is 15 miles ahead of the slower car. The slower car has traveled 230 miles. Find the speeds of the two cars.

A) 30 mph and 33 mph
B) 46 mph and 49 mph
C) 43 mph and 46 mph
D) 48 mph and 51 mph

Question 80

Solve the system of linear equations using matrices.
$$\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.$$

A) $( - 2 , - 4 )$
В) $( - 4 , - 2 )$
C) $( - 2,4 )$
D) $\varnothing$