Question
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges
to mow a lawn that took him
hours to mow.
Which equation models the amount in dollars,
, Troy charges when it takes him h hours to mow a lawn?
A
d=20h
B
h=20d
C
d=45h
D
h=45d
Answers
GPT-4o mini
To determine the correct equation that models the amount Troy charges (\(d\)) based on the time (\(h\)) it takes him to mow a lawn, we need to understand the relationship given in the problem.
The problem states that "the amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn." This means we can express the relationship as:
\[
d = k \cdot h
\]
where \(k\) is the constant of proportionality.
Now, to find the right answer, we need to identify the specific values for \(k\).
Assuming from the context of the question, if it said that Troy charges a specific amount for a specific time, let's say he charges $20 for 1 hour, then \(k = 20\), leading to:
\[
d = 20h
\]
And if it said he charges $45 for some time, it would lead to:
\[
d = 45h
\]
Since we do not have specific values provided in the question for how much he charges or how long he took, we cannot definitively determine the correct equation without that information.
However, if we assume \(k\) could be either 20 or 45 based on the options given, we can analyze the choices.
From the options:
- A: \(d=20h\)
- B: \(h=20d\) (not proportional, this reverses the relationship)
- C: \(d=45h\)
- D: \(h=45d\) (not proportional, this reverses the relationship)
Both A and C are valid equations for different values of \(k\).
Thus, if not given specific charge amounts, A (\(d=20h\)) or C (\(d=45h\)) could be correct depending on the specific values provided in the question. Please clarify the values mentioned for us to pick the right equation. However, among the provided options based on a common understanding, option A (\(d=20h\)) is typically seen as a standard proportional model unless the specific charge rates indicate otherwise.
So ultimately, either A or C can be deemed as correct if we don't have a specific charge amount to go off of.
The problem states that "the amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn." This means we can express the relationship as:
\[
d = k \cdot h
\]
where \(k\) is the constant of proportionality.
Now, to find the right answer, we need to identify the specific values for \(k\).
Assuming from the context of the question, if it said that Troy charges a specific amount for a specific time, let's say he charges $20 for 1 hour, then \(k = 20\), leading to:
\[
d = 20h
\]
And if it said he charges $45 for some time, it would lead to:
\[
d = 45h
\]
Since we do not have specific values provided in the question for how much he charges or how long he took, we cannot definitively determine the correct equation without that information.
However, if we assume \(k\) could be either 20 or 45 based on the options given, we can analyze the choices.
From the options:
- A: \(d=20h\)
- B: \(h=20d\) (not proportional, this reverses the relationship)
- C: \(d=45h\)
- D: \(h=45d\) (not proportional, this reverses the relationship)
Both A and C are valid equations for different values of \(k\).
Thus, if not given specific charge amounts, A (\(d=20h\)) or C (\(d=45h\)) could be correct depending on the specific values provided in the question. Please clarify the values mentioned for us to pick the right equation. However, among the provided options based on a common understanding, option A (\(d=20h\)) is typically seen as a standard proportional model unless the specific charge rates indicate otherwise.
So ultimately, either A or C can be deemed as correct if we don't have a specific charge amount to go off of.