Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A certain factory produces and sells 8000 cars per month, making a monthly net profit of
P dollars. They sell each car for
n dollars and it costs them
c dollars to produce a single car.
Write an equation that relates
P,
n, and
c.

A certain factory produces and sells $8000$ cars per month, making a monthly net profit of $P$ dollars. They sell each car for $n$ dollars and it costs them $c$ dollars to produce a single car. $\newline$ Write an equation that relates $P$ , $n$ , and $c$ .

View step-by-step help

View step-by-step help

Write and solve equations for proportional relationships

Full solution

Q. A certain factory produces and sells

8000

cars per month, making a monthly net profit of

P

dollars. They sell each car for

n

dollars and it costs them

c

dollars to produce a single car.

\newline

Write an equation that relates

P

,

n

, and

c

.

Define variables: Let's define the variables: $\newline$ - $P$ is the monthly net profit. $\newline$ - $n$ is the selling price per car. $\newline$ - $c$ is the cost to produce a single car. $\newline$ - The number of cars produced and sold per month is $8000$ . $\newline$ The net profit is calculated by subtracting the total cost of production from the total revenue. $\newline$ Total revenue is the number of cars sold multiplied by the selling price per car. $\newline$ Total cost is the number of cars produced multiplied by the cost to produce a single car. $\newline$ Let's calculate the total revenue: $\newline$ Total revenue = Number of cars sold $*$ Selling price per car $\newline$ Total revenue = $8000 \times n$
Calculate total revenue: Now, let's calculate the total cost: $\newline$ Total cost = Number of cars produced $*$ Cost to produce a single car $\newline$ Total cost = $8000 \times c$
Calculate total cost: Next, we will write the equation for the net profit: $\newline$ Net profit $P$ = Total revenue - Total cost $\newline$ $P = (8000 \times n) - (8000 \times c)$
Write net profit equation: We can simplify the equation by factoring out the common factor, which is $8000$ : $\newline$ $P = 8000 \times (n - c)$ $\newline$ This is the equation that relates the monthly net profit $P$ , the selling price per car $n$ , and the cost to produce a single car $c$ .

More problems from Write and solve equations for proportional relationships

Question

25

-meter-long fence that she plans to use to enclose a rectangular garden of width

w

. The fencing will be placed around all four sides of the garden so that its area is

25

\newline

Write an equation in terms of

w

that models the situation.

Posted 10 months ago

Question

Each Christmas elf makes

x

toys in an hour.

n

t

hours to produce

1000

\newline

Write an equation that relates

x, n

t

Posted 10 months ago

Question

A certain factory produces and sells

C

computers per month. It costs

x

dollars to produce a single computer, and the factory sells each computer for

y

dollars. Their monthly net profit is

10

000

\newline

Write an equation that relates

C

x

y

Posted 10 months ago

Question

3

trucks to deliver a total of

T

liters of cement. Each truck can transport

x

liters of cement per trip, and makes a total of

y

\newline

Write an equation that relates

T

x

y

Posted 10 months ago

Question

Dyami planted a palm tree in the back yard of his house several years ago. Initially it was

200

centimeters high and its height increased by

30

centimeters each year. Let

H

be the height of the tree in centimeters

t

years after it was planted. Which of the following best explains the relationship between

t

H

\newline

1

\newline

(A) The relationship is exponential because

H

increases by a factor of

30

t

1

\newline

(B) The relationship is linear because

H

30

t

1

\newline

(C) The relationship is exponential because

H

always increases as

t

\newline

(D) The relationship is linear because

H

200

t

1

Posted 7 months ago

Question

Ehsan is having a big going-out-ofbusiness sale and he wants to advertise his sale. He starts by making a large number of advertising fliers for his sale and gives

5

of his friends many fliers. He asks each of them to give fliers to

2

of their friends the next day, and to tell each of their friends to give fliers to

2

of their friends the day after, and so on. Let

F

be the number of people who will be given fliers on day

t

. Which of the following best explains the relationship between

t

F

\newline

1

\newline

(A) The relationship is linear because the values of

F

always increase as the values of

t

\newline

(B) The relationship is exponential because

F

increases by a factor of

5

t

1

\newline

(C) The relationship is linear because

F

increases by a factor of

5

t

1

\newline

(D) The relationship is exponential because

F

increases by a factor of

2

t

1

Posted 7 months ago

Question

The following table shows a proportional relationship between

. Write an equation to describe the relationship between

Posted 5 months ago

Question

On a set of steps, the first step from the base of the steps is labeled

1

, the second is labeled

2

, and so on. Each step has the same height. The table below shows the step number and step's height from the base of the steps.

\newline

\begin{tabular}{cc}

\newline

Step number & Height from the base (meters) \\

\newline

50

10

\newline

90

18

\newline

110

22

\newline

\newline

Write an equation to describe the relationship between

n

, the step number, and

h

, the height from the base.

\newline

\square

Posted 5 months ago

Question

Jeremy and Robin like to collect nickels. Jeremy has

n

nickels, and Robin has

55

nickels. Together they have a total of

100

nickels. Write an equation to describe this situation.

Posted 2 months ago

Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 1 month ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant