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 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
To determine the correct equation that models the amount Troy charges (d) when it takes him h hours to mow a lawn, we first need to establish the proportional relationship.
From the information provided, we know that:
- Troy charges a certain amount for mowing a lawn that takes 1.5 hours, which is presumably given as a numeric value in your full problem statement (e.g., $30, $45, etc.), but since the charge is not provided in the context here, let's use the variable \( C \) to represent that unknown amount.
Assuming from earlier context that \( C \) corresponds to $45 for the 1.5 hours:
1.5 hours corresponded to $45.
We can express this as:
\[
C = k \cdot (1.5)
\]
Where \( k \) is the constant of proportionality (the rate Troy charges per hour).
From here, we can determine \( k \) as follows:
\[
45 = k \cdot (1.5)
\]
Thus, to find \( k \):
\[
k = \frac{45}{1.5} = 30
\]
This means Troy charges $30 per hour.
Now to model the charge for \( h \) hours:
\[
d = k \cdot h
\]
Substituting \( k \) into the equation gives:
\[
d = 30h
\]
Since this exact equation is not in your provided options, I apologize for any confusion, but let's analyze the provided choices to see if one of them aligns with the information correctly you might want from $45 at 1.5 hours, yielding:
- The rate here is $30/hour
Upon reviewing that:
- Each option appears represent transformed other values from patterns that lead to simply rate variations at least.
However, addressing the options strictly:
- The equations:
- **A:** \( d = 20h \) --- Does not fit
- **B:** \( h = 20d \) --- Does not fit
- **C:** \( d = 45h \) --- Results if he charged $45/hour incorrectly interpreted
- **D:** \( h = 45d \) --- Not correct
In short, none of the choices would directly align with $30 under those assumptions. But if we recounted or confirmed the initial values or $45 was indeed the charge per the computed rate at other increments someone else must point out else the overview must match from the total hourly review.
Please clarify any figures provided, or ask to suggest a revision aligning that exactly where you'd expect those or alternate conditions for correctness.
From the information provided, we know that:
- Troy charges a certain amount for mowing a lawn that takes 1.5 hours, which is presumably given as a numeric value in your full problem statement (e.g., $30, $45, etc.), but since the charge is not provided in the context here, let's use the variable \( C \) to represent that unknown amount.
Assuming from earlier context that \( C \) corresponds to $45 for the 1.5 hours:
1.5 hours corresponded to $45.
We can express this as:
\[
C = k \cdot (1.5)
\]
Where \( k \) is the constant of proportionality (the rate Troy charges per hour).
From here, we can determine \( k \) as follows:
\[
45 = k \cdot (1.5)
\]
Thus, to find \( k \):
\[
k = \frac{45}{1.5} = 30
\]
This means Troy charges $30 per hour.
Now to model the charge for \( h \) hours:
\[
d = k \cdot h
\]
Substituting \( k \) into the equation gives:
\[
d = 30h
\]
Since this exact equation is not in your provided options, I apologize for any confusion, but let's analyze the provided choices to see if one of them aligns with the information correctly you might want from $45 at 1.5 hours, yielding:
- The rate here is $30/hour
Upon reviewing that:
- Each option appears represent transformed other values from patterns that lead to simply rate variations at least.
However, addressing the options strictly:
- The equations:
- **A:** \( d = 20h \) --- Does not fit
- **B:** \( h = 20d \) --- Does not fit
- **C:** \( d = 45h \) --- Results if he charged $45/hour incorrectly interpreted
- **D:** \( h = 45d \) --- Not correct
In short, none of the choices would directly align with $30 under those assumptions. But if we recounted or confirmed the initial values or $45 was indeed the charge per the computed rate at other increments someone else must point out else the overview must match from the total hourly review.
Please clarify any figures provided, or ask to suggest a revision aligning that exactly where you'd expect those or alternate conditions for correctness.