Deck 3: Systems of Linear Equations

Question 1

Solve the system by the substitution method.
$$\left\{ \begin{aligned}x & = - 4 y + 4 \\7 x - 5 y & = - 5\end{aligned} \right.$$

A) $\{ ( 1,0 ) \}$
B) $\{ ( x , y ) \mid x = - 4 y + 4 \}$
C) $\{ ( 0,1 ) \}$
D) $\varnothing$

Answer 1

C

Question 2

Determine whether the given ordered pair is a solution to the system.
$$\begin{array} { l } ( 6,2 ) \\\left\{ \begin{array} { l } y = 2 \\x = 3 y\end{array} \right.\end{array}$$

A) not a solution
B) solution

Answer 2

B

Question 3

Solve the system by the substitution method.
$$\left\{ \begin{array} { l } x + y = - 7 \\x - y = 15\end{array} \right.$$

A) $\varnothing$
B) $\{ ( 4 , - 11 ) \}$
C) $\{ ( x , y ) \mid x + y = - 7 \}$
D) $\{ ( 4,11 ) \}$

Answer 3

B

Question 4

Solve the problem.
The graph shows the results of an ongoing survey of 500 random students at State University from 2007 through 2012. The survey asked whether students bought the majority of their music on CD or if they downloaded the majority of their music as MP3 files from the internet. Use the graph to estimate the point of intersection. In what year was the number of students who bought the majority of their music on CDs and the number of students who downloaded the majority of their music as MP3 files the same? How many students were there for each? A) (2011, 250); 2011; 250 students B) (2010, 300); 2011; 300 students C) (2010, 250); 2010; 250 students D) (2011, 200); 2011; 200 students

Question 5

Determine whether the given ordered pair is a solution to the system.
$$\begin{array} { l } ( - 1,3 ) \\\left\{ \begin{array} { l } 3 x + y = - 6 \\4 x + 3 y = - 13\end{array} \right.\end{array}$$

A) solution
B) not a solution

Question 6

Solve the system by graphing.
A) $\{ ( 2,1 ) \}$
B) $\varnothing$
C) $\{ ( x , y ) \mid 3 x - 2 y = 4 \}$
D) $\{ ( 1,2 ) \}$

Question 7

Solve the system by the substitution method.
$$\left\{ \begin{array} { r } x + 7 y = - 2 \\3 x + y = 34\end{array} \right.$$

A) $\varnothing$
B) $\{ ( x , y ) \mid x + 7 y = - 2 \}$
C) $\{ ( 12 , - 2 ) \}$
D) $\{ ( - 2,3 ) \}$

Question 8

Determine whether the given ordered pair is a solution to the system.
$$\left\{ \begin{array} { l } ( 6 , - 2 ) \\3 x + y = 16 \\2 x + 3 y = 6\end{array} \right.$$

A) solution
B) not a solution

Question 9

Solve the system by graphing.
A) $\{ ( 1,1 ) \}$
B) $\{ ( x , y ) \mid y + x = 6 \}$
C) $\{ ( 1,5 ) \}$
D) $\varnothing$

Question 10

Solve the system by graphing.
$$\left\{ \begin{aligned}y - 6 x & = 5 \\6 y & = 36 x + 30\end{aligned} \right.$$

A) $\{ ( 1,1 ) \}$
B) $\varnothing$
C) $\{ ( - 1.5 , - 1 ) \}$
D) $\{ ( x , y ) \mid y - 6 x = 5 \}$

Question 11

Determine whether the given ordered pair is a solution to the system.
$$\begin{array} { l } ( - 6,2 ) \\\left\{ \begin{array} { l } x + y = 8 \\x - y = 4\end{array} \right.\end{array}$$

A) solution
B) not a solution

Question 12

Solve the system by the substitution method.
$$\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.$$

A) $\{ ( x , y ) \mid 2 x + y = 30 \}$
B) $\{ ( 10,10 ) \}$
C) $\varnothing$
D) $\{ ( 0,10 ) \}$

Question 13

Solve the system by graphing.
$$\left\{ \begin{array} { l } 5 x + y = - 20 \\2 x + 4 y = 10\end{array} \right.$$

A) $\{ ( - 5,5 ) \}$
B) $\{ ( x , y ) \mid 5 x + y = - 20 \}$
C) $\{ ( 5,5 ) \}$
D) $\varnothing$

Question 14

Solve the system by graphing.

A) {(0, 14)}
B) Ø
C) {(5, -6)}
D) {(x, y) 4x + y = 14}

Question 15

Solve the system by graphing.
$$\left\{ \begin{array} { l } 3 x + y = 13 \\3 x + y = 28\end{array} \right.$$

A) {(9, 4)}
B) Ø
C) {(x, y) 3x + y = 13}
D) {(6, 10)}

Question 16

Determine whether the given ordered pair is a solution to the system.
$$\begin{array} { l } ( - 6,2 ) \\\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 8\end{array} \right.\end{array}$$

A) solution
B) not a solution

Question 17

Solve the system by the substitution method.
$$\left\{ \begin{aligned}y & = - 3 x + 13 \\2 x + 9 y & = - 8\end{aligned} \right.$$

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

Question 18

Solve the system by graphing.
$$\left\{ \begin{array} { l } 3 x + 3 y = 33 \\2 x + 3 y = 28\end{array} \right.$$

A) $\{ ( 5,6 ) \}$
B) $\{ ( x , y ) \mid 3 x + 3 y = 33 \}$
C) $\{ ( 6,5 ) \}$
D) $\varnothing$

Question 19

Solve the system by the substitution method.
$$\left\{ \begin{array} { r } 5 x - 2 y = - 1 \\x + 4 y = 35\end{array} \right.$$

A) $\{ ( 3,8 ) \}$
B) $\{ ( 3,9 ) \}$
C) $\{ ( x , y ) \mid x + 4 y = 35 \}$
D) $\varnothing$

Question 20

Solve the system by the substitution method.
$$\left\{ \begin{array} { r r } 9 x + y = & 0 \\- 9 x + y = & - 18\end{array} \right.$$

A) $\varnothing$
В) $\{ ( 1 , - 9 ) \}$
C) $\{ ( x , y ) \mid 9 x + y = 0 \}$
D) $\{ ( - 1,9 ) \}$

Question 21

Solve the system by any method.
$$\left\{ \begin{array} { l } 7 x - 3 y = 8 \\28 x - 12 y = 16\end{array} \right.$$

A) $( 8,16 )$
B) $\{ ( x , y ) \mid 7 x - 3 y = 8 \}$
C) $\left( \frac { 24 } { 35 } , - \frac { 8 } { 5 } \right)$
D) $\varnothing$

Question 22

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 5 x + 7 y = 54 \\5 x + 2 y = 69\end{array} \right.$$

A) $\varnothing$
B) $\{ ( - 15,5 ) \}$
C) $\{ ( 15 , - 3 ) \}$
D) $\{ ( x , y ) \mid 5 x + 2 y = 69 \}$

Question 23

Solve the system by any method.
$$\left\{ \begin{array} { l } 9 x + 6 y = - 27 \\8 x - 8 y = 96\end{array} \right.$$

A) $\varnothing$
B) $( 3 , - 9 )$
C) $( - 3 , - 8 )$
D) $( 2 , - 8 )$

Question 24

Solve the system by any method.
$$\left\{ \begin{array} { l } 3 x - 9 y = 7 \\- 6 x + 18 y = - 28\end{array} \right.$$

A) $\varnothing$
B) $\left( \frac { 1 } { 7 } , - \frac { 3 } { 7 } \right)$
C) $( 3,7 )$
D) $( 2,4 )$

Question 25

Solve the system by any method.
$$\left\{ \begin{array} { l } 8 x - 82 = - 6 y \\6 x + 4 y = 60\end{array} \right.$$

A) $\{ ( x , y ) \mid 8 x - 82 = - 6 y \}$
B) $( 8,4 )$
C) $( 8,3 )$
D) $( 7,4 )$

Question 26

Solve the system by the substitution method.
$$\left\{ \begin{array} { l } 2 x + y = 10 \\2 x + y = 18\end{array} \right.$$

A) $\{ ( 2,8 ) \}$
B) $\{ ( x , y ) \mid 2 x + y = 10 \}$
C) $\{ ( 4,6 ) \}$
D) $\varnothing$

Question 27

Solve the system by the substitution method.
$$\left\{ \begin{array} { l } \frac { x } { 3 } - \frac { y } { 6 } = 1 \\\frac { x } { 7 } - y = 6\end{array} \right.$$

A) $( - 6,0 )$
B) $( 0 , - 6 )$
C) $( 6,0 )$
D) $( 0,6 )$

Question 28

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 3 x - 5 y = - 12 \\6 x + 8 y = - 24\end{array} \right.$$

A) $\varnothing$
B) $\{ ( 4,0 ) \}$
C) $\{ ( - 4,0 ) \}$
D) $\{ ( x , y ) \mid 3 x - 5 y = - 12 \}$

Question 29

Solve the system by the substitution method.
$$\left\{ \begin{array} { l } 3 x + y = 11 \\9 x + 3 y = 33\end{array} \right.$$

A) $\{ ( 0,11 ) \}$
B) $\{ ( x , y ) \mid 3 x + y = 11 \}$
C) $\varnothing$
D) $\{ ( 5 , - 4 ) \}$

Question 30

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 3 x + y = 14 \\3 x + y = 26\end{array} \right.$$

A) $\{ ( x , y ) \mid 3 x + y = 14 \}$
B) $\varnothing$
C) $\{ ( 12,2 ) \}$
D) $\{ ( 8,11 ) \}$

Question 31

Solve the system by the addition method.
$$\left\{ \begin{array} { r } 8 x - 7 y = 6 \\- 32 x + 28 y = - 18\end{array} \right.$$

A) $\left( 2 , - \frac { 7 } { 4 } \right)$
B) $( 4,3 )$
C) $\{ ( x , y ) \mid 8 x - 7 y = 6 \}$
D) $\varnothing$

Question 32

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 5 x - 2 y = - 1 \\7 x + 4 y = 53\end{array} \right.$$

A) $\varnothing$
B) $\{ ( 3,8 ) \}$
C) $\{ ( 3,9 ) \}$
D) $\{ ( x , y ) \mid 5 x - 2 y = - 1 \}$

Question 33

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 6 x + 27 y = 27 \\5 x - 9 y = - 9\end{array} \right.$$

A) $\varnothing$
B) $\{ ( x , y ) \mid 5 x - 9 y = - 9 \}$
C) $\{ ( 0,1 ) \}$
D) $\{ ( 1,0 ) \}$

Question 34

Solve the problem.
A company's expenses included many factors. In 2012, travel costs were 2.62% of the expense budget, increasing by 0.22% of the total expense budget per year. In 2012, office supplies were 5.71% of the expense budget, increasing by 0.05% of the total expense budget per year. Write a system of equations with two functions. Write one function that models the cost of travel as a percentage of the total expense budget x years after 2012, and another function that models the cost of office supplies as a percentage of the total expense budget x years after 2012. A) $y = 2.62 x + 0.22$
$y = 5.71 x + 0.22$
B) $y = - 0.22 x + 2.62$
$y = - 0.05 x + 5.71$
C) $y = 0.22 x$
$y = 0.05 x$
D) $y = 0.22 x + 2.62$
$y = 0.05 x + 5.71$

Question 35

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 6 x + 3 y = 51 \\2 x - 6 y = 38\end{array} \right.$$

A) $\{ ( x , y ) \mid 2 x - 6 y = 38 \}$
B) $\{ ( - 3,10 ) \}$
C) $\{ ( 10 , - 3 ) \}$
D) $\varnothing$

Question 36

Solve the system by the addition method.
$$\left\{ \begin{array} { l } 3 x + 6 y = 3 \\2 x + 9 y = - 8\end{array} \right.$$

A) $\{ ( - 5,2 ) \}$
B) $\{ ( x , y ) \mid 3 x + 6 y = 3 \}$
C) $\{ ( 5 , - 2 ) \}$
D) $\varnothing$

Question 37

Solve the problem.
A company's expenses included many factors. In 2012, travel costs were 2.97% of the expense budget , increasing by 0.21% of the total expense budget per year. In 2012, office supplies were 5.80% of the expense budget, increasing by 0.03% of the total expense budget per year. In which year will the cost of travel expenses and office supplies be the same? For that year, what will be the cost of each expense as a percentage of the total expense budget?

A) 2030; 6.8
B) 2028; 6.3
C) 2027; 6.1
D) 2026; 5.9

Question 38

Solve the system by the addition method.
$$\left\{ \begin{array} { r } 3 x + y = 10 \\12 x + 4 y = 40\end{array} \right.$$

A) $\{ ( 0,10 ) \}$
B) $\varnothing$
C) $\{ ( 5 , - 5 ) \}$
D) $\{ ( x , y ) \mid 3 x + y = 10 \}$

Question 39

Solve the system by any method.
$$\left\{ \begin{array} { l } 9 x = 22 - 8 y \\- 4 x + 3 y = 23\end{array} \right.$$

A) $( - 2,5 )$
В) $( - 3,6 )$
C) $\varnothing$
D) $( - 2,6 )$

Question 40

Solve the system by the addition method.
$$\left\{ \begin{array} { r } 5 x + 6 y = - 7 \\- 5 x - 13 y = 21\end{array} \right.$$

A) $\{ ( - 1,2 ) \}$
B) $\{ ( x , y ) \mid 5 x + 6 y = - 7 \}$
C) $\varnothing$
D) $\{ ( 1 , - 2 ) \}$

Question 41

Solve the problem.
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 10 feet more than 2 times the width. He needs 68 feet of fencing to do the job. Find the length and width of the garden. A) length: $26 \mathrm { ft }$ ; width: $8 \mathrm { ft }$
B) length: $24 \mathrm { ft }$ ; width: $7 \mathrm { ft }$
C) length: $48 \frac { 2 } { 3 } \mathrm { ft }$ ; width: $19 \frac { 1 } { 3 } \mathrm { ft }$
D) length: $28 \mathrm { ft }$ ; width: $9 \mathrm { ft }$

Question 42

Solve the problem.
Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } C ( x ) = 6000 x + 24,000 \\R ( x ) = 8000 x\end{array}$$

A) $P ( x ) = 2000 x - 24,000$
B) $P ( x ) = - 2000 x + 24,000$
C) $\mathrm { P } ( \mathrm { x } ) = - 2000 \mathrm { x } - 24,000$
D) $P ( x ) = 2000 x + 24,000$

Question 43

Solve the problem.
A chemist needs 150 milliliters of a 45% solution but has only 25% and 55% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

A) 100 milliliters of 25%; 50 milliliters of 55%
B) 60 milliliters of 25%; 100 milliliters of 55%
C) 50 milliliters of 25%; 100 milliliters of 55%
D) 60 milliliters of 25%; 110 milliliters of 55%

Question 44

Solve the system by any method.
$$\left\{ \begin{array} { r } 3 x + y = 2 \\- 12 x - 4 y = - 8\end{array} \right.$$

A) infinitely many solutions
B) one ordered-pair solution
C) no solution

Question 45

Solve the problem.
An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 74x + 250, where x is the number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to solve the system and choose the statement that most accurately describes the solution. A) At some point between 2003 and 2011, the company had sold 1800 of each product. B) The company sold about 1.8 times as many of Product B as Product A. C) When 383,000 of Product A had been sold, 1.8 times as many of Product B had been sold. D) At about 1.8 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B.

Question 46

Solve the system by any method.
$$\left\{ \begin{array} { l } - 3 x + 2 y = 2 \\4 y = 4 + 6 x\end{array} \right.$$

A) $\varnothing$
B) $( - 3,2 )$
C) $\{ ( x , y ) \mid - 3 x + 2 y = 2 \}$
D) $( 0,0 )$

Question 47

Solve the problem.
Julie and Eric row their boat (at a constant speed) 24 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 6 hours. Find the rate of the current.

A) 2 mph
B) 1 mph
C) 0.5 mph
D) 5 mph

Question 48

Solve the problem.
A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $120 for the truck and $55 per hour for the movers. Company B charges $110 for the truck and $70 per hour for the movers. Create a cost equation for each company where y is the total cost and x is the number of hours of labor. Write a system of equations.

A) 55y = 120x
B) 55y = x + 120
C) y = 55x + 120
D) y = 120x + 55 70y = 110x 70y = x + 110 y = 70x + 110 y = 110x + 70

Question 49

Solve the problem.
A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 6 inches longer than the width. Find the width.

A) 11 in.
B) 28 in.
C) 17 in.
D) 23 in.

Question 50

Solve the problem.
One number is 3 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

A) 4 and 7
B) 5 and 8
C) -7 and -4
D) 3 and 6

Question 51

Solve the problem.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.00. Another customer buys 5 hot dogs and 4 bags of potato chips for $13.75. Find the cost of each item.

A) $2.00 for a hot dog; $1.50 for a bag of potato chips
B) $1.75 for a hot dog; $1.50 for a bag of potato chips
C) $1.25 for a hot dog; $1.75 for a bag of potato chips
D) $1.75 for a hot dog; $1.25 for a bag of potato chips

Question 52

Solve the problem.
A twin-engined aircraft can fly 672 miles from city A to city B in 3 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

A) 96 mph
B) 48 mph
C) 80 mph
D) 64 mph

Question 53

Solve the problem.
A bank teller has 53 $20 and $5 bills in her cash drawer. The value of the bills is $490. How many $20 bills are there?

A) 38 $20 bills
B) 36 $20 bills
C) 17 $20 bills
D) 15 $20 bills

Question 54

Solve the problem.
Andrea is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $190 for materials and equipment rental plus $50 per hour for labor. Company B gave an estimate of $260 for materials and equipment rental plus $40 per hour for labor. Create a cost equation for each company where y is the total cost of the landscaping and x is the number of hours of labor. Determine how many hours of labor will be required for the two companies to cost the same.

A) 11 hr
B) 10 hr
C) 6 hr
D) 7 hr

Question 55

Solve the problem.
A retired couple has $170,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,700 per year?

A) $120,000 at 11% and $50,000 at 5%
B) $110,000 at 5% and $60,000 at 11%
C) $120,000 at 5% and $50,000 at 11%
D) $130,000 at 11% and $40,000 at 5%

Question 56

Solve the problem.
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $3.40 more than the value of the nickels. How many nickels and dimes does Jamil have?

A) 3 nickels and 27 dimes
B) 5 nickels and 45 dimes
C) 4 nickels and 36 dimes
D) 36 nickels and 4 dimes

Question 57

Solve the system by any method.
$$\left\{ \begin{array} { l } \frac { x } { 2 } + \frac { y } { 3 } = 4 \\\frac { x } { 4 } + \frac { y } { 6 } = 2\end{array} \right.$$

A) one ordered-pair solution
B) infinitely many solutions
C) no solution

Question 58

Solve the problem.
One number is 4 less than a second number. Twice the second number is 17 more than 3 times the first. Find the two numbers.

A) 5 and 9
B) -10 and -6
C) -8 and -4
D) -9 and -5

Question 59

Solve the problem.
Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $170. The cost of a child's ticket was $5 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

A) adult's ticket: $18; child's ticket: $13
B) adult's ticket: $20; child's ticket: $15
C) adult's ticket: $17; child's ticket: $12
D) adult's ticket: $19; child's ticket: $14

Question 60

Solve the problem.
A college student earned $8400 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 8%. If the student received a total of $720 in interest at the end of the year, how much was invested at 10%?

A) $4200
B) $1050
C) $2400
D) $6000

Question 61

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea
$$\begin{array} { l } C ( x ) = 14 x + 24,000 \\R ( x ) = 34 x\end{array}$$

A) 1200 units
B) 445 units
C) 1201 units
D) 1202 units en.

Question 62

Determine if the given ordered triple is a solution of the system.
$$\left\{ \begin{array} { l } 5 , - 2,3 ) \\x + y + z = 6 \\x - y + 4 z = 19 \\5 x + y + z = 26\end{array} \right.$$

A) solution
B) not a solution

Question 63

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

What is the profit when 878 binoculars are produced?

A) $3256
B) $2012
C) $256
D) $5012

Question 64

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary.
$$\begin{array} { l } C ( x ) = 1.7 x + 700 \\R ( x ) = 2.7 x\end{array}$$

A) $\$ 700$
B) $\$ 1890$
C) $\$ 266$
D) $\$ 430$

Question 65

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary.
$$\begin{array} { l } C ( x ) = 8000 x + 90,000 \\R ( x ) = 17,000 x\end{array}$$

A) $\$ 170,000$
B) $\$ 10$
C) $\$ 80,000$
D) $\$ 61,200$

Question 66

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea
$$\begin{array} { l } C ( x ) = 56 x + 900 \\R ( x ) = 71 x\end{array}$$

A) 62 units
B) 60 units
C) 61 units
D) 11 units en.

Question 67

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

How many binoculars must be produced and sold for the company to break even?

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

Question 68

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

More than how many binoculars must be produced and sold for the company to have a profit gain?

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

Question 69

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

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

Question 70

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

Is there a profit when 676 binoculars are produced?

A) Yes
B) No

Question 71

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea
$$\begin{array} { l } C ( x ) = 7000 x + 63,000 \\R ( x ) = 14,000 x\end{array}$$

A) 11 units
B) 4 units
C) 9 units
D) 10 units en.

Question 72

Solve the problem.
Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } C ( x ) = 0.4 x + 450 \\R ( x ) = 0.9 x\end{array}$$

A) $P ( x ) = 0.5 x - 450$
B) $P ( x ) = 0.5 x + 450$
C) $P ( x ) = - 0.5 x - 450$
D) $P ( x ) = - 0.5 x + 450$

Question 73

Solve the problem.
Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } C ( x ) = 59 x + 1430 \\R ( x ) = 70 x\end{array}$$

A) $P ( x ) = - 11 x + 1430$
B) $P ( x ) = - 11 x - 1430$
C) $P ( x ) = 11 x - 1430$
D) $P ( x ) = 11 x + 1430$

Question 74

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea
$$\begin{array} { l } C ( x ) = 1.3 x + 840 \\R ( x ) = 1.9 x\end{array}$$

A) 1400 units
B) 1420 units
C) 337 units
D) 1410 units en.

Question 75

Determine if the given ordered triple is a solution of the system.
$$\left\{ \begin{array} { c } ( - 3,2,3 ) \\x + y + z = 2 \\x - y + 2 z = - 5\end{array} \right.$$

A) solution
B) not a solution

Question 76

Solve the problem.
Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary.
$$\begin{array} { l } C ( x ) = 76 x + 3080 \\R ( x ) = 104 x\end{array}$$

A) $\$ 1128$
B) $\$ 11,440$
C) $\$ 110$
D) $\$ 1780$

Question 77

Determine if the given ordered triple is a solution of the system.
$$\left\{ \begin{array} { c } ( 0 , - 4 , - 3 ) \\3 x - y + 5 z = - 11 \\x + z = - 3 \\x + 2 y + z = - 11\end{array} \right.$$

A) not a solution
B) solution

Question 78

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

Is there a profit when 966 binoculars are produced?

A) Yes
B) No

Question 79

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

Use the revenue and cost functions to write the profit function from producing and selling x binoculars.

A) P(x) = 4x + 1500
B) P(x) = 2x - 1500
C) P(x) = 4x - 1500
D) P(x) = 2x + 1500

Question 80

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

At the break-even point both cost and revenue are what?

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