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

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.