Question
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges 30
to mow a lawn that took him 1.5
hours to mow.
Which equation models the amount in dollars,
, Troy charges when it takes him h hours to mow a lawn?
A
d=20hd=20hd=20h
B
h=20dh=20dh=20d
C
d=45hd=45hd=45h
D
h=45dh=45dh=45d
Answers
GPT-4o mini
Since the amount Troy charges is proportional to the time it takes him to mow the lawn, we can express this relationship with the equation:
\[
d = kh
\]
where:
- \( d \) is the amount charged in dollars,
- \( h \) is the time taken in hours,
- \( k \) is the constant of proportionality.
From the problem, we know that when \( h = 1.5 \) hours, \( d = 30 \) dollars. We can find \( k \) using these values:
\[
30 = k \cdot 1.5
\]
To find \( k \), we can rearrange the equation:
\[
k = \frac{30}{1.5} = 20
\]
Now, we can insert the value of \( k \) back into the original equation:
\[
d = 20h
\]
Thus, the equation that models the amount in dollars Troy charges when it takes him \( h \) hours to mow a lawn is:
\[
d = 20h
\]
Therefore, the correct answer is:
**A. \( d = 20h \)**
\[
d = kh
\]
where:
- \( d \) is the amount charged in dollars,
- \( h \) is the time taken in hours,
- \( k \) is the constant of proportionality.
From the problem, we know that when \( h = 1.5 \) hours, \( d = 30 \) dollars. We can find \( k \) using these values:
\[
30 = k \cdot 1.5
\]
To find \( k \), we can rearrange the equation:
\[
k = \frac{30}{1.5} = 20
\]
Now, we can insert the value of \( k \) back into the original equation:
\[
d = 20h
\]
Thus, the equation that models the amount in dollars Troy charges when it takes him \( h \) hours to mow a lawn is:
\[
d = 20h
\]
Therefore, the correct answer is:
**A. \( d = 20h \)**