Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Austin is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let
C represent the total cost, in dollars, of producing
p phones in a given day. A graph of
C is shown below. Write an equation for
C then state the slope of the graph and determine its interpretation in the context of the problem.
Answer Attempt 1 out of 2

C=
◻
The slope of the function is
◻ which represents

Austin is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let $C$ represent the total cost, in dollars, of producing $p$ phones in a given day. A graph of $C$ is shown below. Write an equation for $C$ then state the slope of the graph and determine its interpretation in the context of the problem. $\newline$ Answer Attempt $1$ out of $2$ $\newline$ $C=$ $\square$ $\newline$ The slope of the function is $\square$ which represents

View step-by-step help

View step-by-step help

Find a value using two-variable equations: word problems

Full solution

Q. Austin is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let

C

represent the total cost, in dollars, of producing

p

phones in a given day. A graph of

C

is shown below. Write an equation for

C

then state the slope of the graph and determine its interpretation in the context of the problem.

\newline

Answer Attempt

1

out of

2

\newline

C=

\square

\newline

The slope of the function is

\square

which represents

Start Point and Fixed Cost: The graph typically starts at a point on the y-axis, which represents the fixed cost (let's call it $F$ ). This is the cost Austin pays regardless of the number of phones produced. The graph then rises with a constant slope, which represents the variable cost per phone (let's call it $v$ ). The equation for a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. In this context, $C = vp + F$ .
Calculating the Slope: To find the slope $v$ , we need two points on the graph. Let's say the graph passes through $(p_1, C_1)$ and $(p_2, C_2)$ . The slope $v$ is calculated as $(C_2 - C_1) / (p_2 - p_1)$ . This slope represents the cost per phone for materials and labor.
Finding the Y-Intercept: The y-intercept $F$ is the point where the line crosses the y-axis, which occurs when $p = 0$ . This is the daily fixed cost for renting the building and equipment.
Example Calculation: Now, let's assume the graph provided specific points or values for the slope and y-intercept. For example, if the graph shows that the fixed cost is $\$100$ and the cost per phone is $\$5$ , the equation would be $C = 5p + 100$ .
Interpreting the Slope: The slope of the function is $5$ , which represents the cost per phone for materials and labor. This means for every additional phone produced, the total cost increases by $\$5$ .

More problems from Find a value using two-variable equations: word problems

Question

This equation shows how the distance traveled by a car is related to the time spent driving.

d = 50t + 10

t

represents the time in hours, and the variable

d

represents the distance in miles. How far does the car travel in

2

Posted 3 months ago

Question

The equation shows how the cost of buying pencils is related to the number of pencils purchased.

\newline

c= 0.5p+2

\newline

p

represents the number of pencils, and the variable

c

represents the total cost. How much does it cost to buy

10

Posted 3 months ago

Question

This equation shows how the total score in a game is related to the number of points scored per level.

s = 100l + 250

l

represents the levels completed, and the variable

s

represents the total score. What is the total score after completing

3

Posted 1 month ago

Question

The equation shows how the amount of paint needed is related to the area to be painted.

p = 2a + 5

a

represents the area in square meters, and the variable

p

represents the amount of paint in liters. How much paint is needed for an area of

8

Posted 1 month ago

Question

This equation shows how the total bill for a meal is related to the number of people sharing the meal.

\newline

b = 15n + 35

\newline

n

represents the number of people, and the variable

b

represents the total bill. What is the total bill for a meal shared by

4

Posted 3 months ago

Question

Poppy the dog weighs

p

pounds, and Yumi the cat weighs

y

pounds. If Poppy weighs

36

more pounds than Yumi does, which of the following equations correctly describes the relationship between their weights?

\newline

1

\newline

p+y=36

\newline

p+36=y

\newline

p-y=36

\newline

y-p=36

Posted 1 month ago

Question

Calvin and Melvin are two of Santa's elves. The number of toys they build is given by

11 c+8 m

c

is the number of candy canes Calvin eats for breakfast and

m

is the number of candy canes Melvin eats for breakfast. How many toys do they build when Calvin eats

5

candy canes and Melvin eats

3

candy canes for breakfast?

Posted 1 month ago

Question

2 w+4

\newline

Carly is cutting a piece of paper stock based on the width of a photo. The expression above describes the length of the paper stock, in inches, for a photo that is

w

inches wide. If the photo is

8

5

inches wide, what is the length of the paper stock in inches?

Posted 27 days ago

Question

Calvin and Melvin are two of Santa's elves. The number of toys they build is given by

11 c+8 m

c

is the number of candy canes Calvin eats for breakfast and

m

is the number of candy canes Melvin eats for breakfast.

\newline

How many toys do they build when Calvin eats

5

candy canes and Melvin eats

3

candy canes for breakfast?

\newline

Posted 2 months ago

Question

The approval rating of a certain politician is changing at a rate of

r(t)

percent of the population per month (where

t

is the time in months).

\newline

\int_{0}^{3} r(t) d t

\newline

1

\newline

(A) The rate of change of the approval rating of the politician when

t=3

\newline

(B) The average rate of change of the approval rating during the first three months

\newline

(C) The change in the percent of the population who approves of the politician during the first three months

\newline

(D) The percent of the population who approves of the politician when

t=3

Posted 1 month ago