Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Read the description of a proportional relationship. $\newline$ To help the environment and make some extra money, Dan takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dan brings in for recycling. There is a proportional relationship between the weight (in pounds) of the cans Dan brings into the shop, $x$ , and the amount (in dollars) the shop pays Dan, $y$ . $\newline$ Last month, Dan brought $4$ pounds of cans into the shop and was paid $\$1$ . Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_\_$

View step-by-step help

View step-by-step help

Write and solve equations for proportional relationships

Full solution

Q. Read the description of a proportional relationship.

\newline

To help the environment and make some extra money, Dan takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dan brings in for recycling. There is a proportional relationship between the weight (in pounds) of the cans Dan brings into the shop,

x

, and the amount (in dollars) the shop pays Dan,

y

.

\newline

Last month, Dan brought

4

pounds of cans into the shop and was paid

\$1

. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Identify Given Values: Step $1$ : Identify the given values from the problem description. $\newline$ Dan brought $4$ pounds of cans and received $\$1$ . So, $x = 4$ pounds and $y = \$1$ . $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x} = \frac{1}{4}$
Calculate Constant of Proportionality: Step $2$ : Use the constant of proportionality to write the equation. $\newline$ The equation for the proportional relationship is $y = kx$ . $\newline$ Substitute $k = \frac{1}{4}$ into the equation. $\newline$ $y = \left(\frac{1}{4}\right)x$

More problems from Write and solve equations for proportional relationships

Question

Read the description of a proportional relationship. Every spring, Kenny plants colorful flowers in his garden. This year, he decides to plant petunias. He buys them at the garden store, brings them back home, and starts planting. There is a proportional relationship between the amount of time (in minutes) Kenny has been working in his garden,

x

, and the number of petunias he has planted,

y

. After working in his garden for

2

minutes, Kenny has planted

4

petunias. Write the equation for the relationship between

x

y

y = \_\_\_

Posted 8 months ago

Question

Addison painted her room. She had

50

square meters to paint, and she painted at a constant rate. After

2

hours of painting, she had

35

square meters left.

\newline

y

represent the area (in square meters) left to paint after

x

\newline

Complete the equation for the relationship between the area and number of hours.

\newline

y=

Posted 10 months ago

Question

V=\ell w h

\newline

The formula gives the volume

V

of a right rectangular prism with length

\ell

w

h

. What is the volume, in cubic meters, of a rectangular prism that is

6

2

meters wide, and

10

Posted 10 months ago

Question

20

-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

18

75

\newline

Write an equation in terms of

w

that models the situation.

Posted 3 months ago

Question

On her way home from the laboratory, Duru realized that she left a test tube containing

50

000

bacteria in the lab. Each minute that passes,

\frac{1}{3}

of the total number of bacteria duplicate. If the number of bacteria reaches

100

000

, the test tube will explode! Naturally, she turned around and rushed back to the lab.

\newline

t

minutes to return to the lab, and she found the test tube intact.

\newline

Write an inequality in terms of

t

that models the situation.

Posted 3 months ago

Question

Wilmer went up the hill for

x

minutes at a speed of

y

kilometers per minute. Then he went down the same path at a speed of

z

kilometers per minute, and it took

\operatorname{him} w

minutes to do it.

\newline

Write an equation that relates

x, y

z

w

Posted 7 months ago

Question

A certain factory produces and sells

x

kilograms of ice cream per month. It costs

c

dollars to produce one kilogram of ice cream, which is then sold for

\mathbf{0 . 1 6}

dollars. The factory's monthly net profit is

P

\newline

Write an equation that relates

x, c

P

Posted 7 months ago

Question

x

delivery persons carry a total of

B

bags of groceries up the stairs. They can each carry

y

bags at a time, and they each make

2

trips up the stairs.

\newline

Write an equation that relates

x

B

y

Posted 8 months ago

Question

Fen completed a triathlon race whose total distance is

D

kilometers. First, she swam a distance of

0

5

kilometer. Then, she rode a bicycle for

x

hours at an average speed of

20

kilometers per hour. Finally, she ran for

0

5

hour at an average speed of

v

kilometers per hour.

\newline

Write an equation that relates

D

x

v

Posted 9 months ago

Question

A baker needs more than

120

minutes to let their dough rise.

\newline

Write an inequality that describes

m

, the number of minutes needed for the dough to rise.

Posted 8 months ago

Related topics

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