4. The amount Troy charges to mow a lawn is proportlonal to the time it takes him to mow the lawn. Troy charges $$ \$ 30 $$ to mow a lawn that took him 1.6 houra to mow. Which equatlon modets the nmount in doltars, of, Troy charges whon it takes him h hours to mow a lawn? A. $$ \quad d=20 h $$ B. $$ h=20 d $$ C. $$ \quad d=45 h $$ D. $$ h=45 d

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4. The amount Troy charges to mow a lawn is proportlonal to the time it takes him to mow the lawn. Troy charges $$ \$ 30 $$ to mow a lawn that took him 1.6 houra to mow. Which equatlon modets the nmount in doltars, of, Troy charges whon it takes him h hours to mow a lawn? A. $$ \quad d=20 h $$ B. $$ h=20 d $$ C. $$ \quad d=45 h $$ D. $$ h=45 d< $$ wreng work

UpStudy AI · Accepted Answer

To solve the problem, we need to establish the relationship between the amount Troy charges (in dollars) and the time it takes him to mow a lawn (in hours).

### Step 1: Identify the known conditions
- Troy charges $$ \$30 $$ for mowing a lawn.
- The time taken to mow the lawn is $$ 1.6 $$ hours.

### Step 2: Establish the proportional relationship
Since the amount charged is proportional to the time taken, we can express this relationship as:
$$
d = k \cdot h
$$
where:
- $$ d $$ is the amount charged in dollars,
- $$ h $$ is the time in hours,
- $$ k $$ is the constant of proportionality.

### Step 3: Find the constant of proportionality $$ k $$
Using the known values:
$$
30 = k \cdot 1.6
$$
To find $$ k $$, we can rearrange the equation:
$$
k = \frac{30}{1.6}
$$

Now, let's calculate $$ k $$:
$$
k = \frac{30}{1.6} = 18.75
$$

### Step 4: Write the equation
Now that we have $$ k $$, we can substitute it back into the proportional relationship:
$$
d = 18.75h
$$

### Step 5: Compare with the options
Now we need to check which of the provided options matches our derived equation $$ d = 18.75h $$.

The options given are:
A. $$ d = 20h $$  
B. $$ h = 20d $$  
C. $$ d = 45h $$  
D. $$ h = 45d $$

None of the options directly match $$ d = 18.75h $$. However, if we consider the closest option, we can see that none of them are correct.

### Conclusion
The correct equation that models the amount Troy charges when it takes him $$ h $$ hours to mow a lawn is:
$$
d = 18.75h
$$
Since none of the provided options are correct, the answer is not listed among the choices.
The correct equation is $$ d = 18.75h $$, which is not among the provided options.

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