Question

The amount Diego charges to detail an SUV is proportional to the time it takes him to detail the vehicle. Diego charges $37.50 to detail a SUV that takes 2.5 hours to complete. Which equation models the amount in dollars, d, Diego charges when it takes him h hours to detail the vehicleA: h = 15dB: d = 15hC: d = 93.75hD: h = 93.75

Answer 1

B: d=15h

Step-by-step explanation

Step 1

as it is proportional we an use a rule of three.

Diego charges $37.50 to detail a SUV that takes 2.5 hours to complete.

then, find the proportion

`\begin{gathered} 37.5\Rightarrow2.5 \\ \text{the proportion is} \\ \frac{37.5\text{ dollars}}{2.5\text{ hours}}=15\text{ dollars per hour} \end{gathered}`

Step 2

Let

h represents the times in hours

and

d represents the amount in dollars

then,the proportion is

`\text{Proportion}=(d)/(h)`

the proportions must be the same, then

`(d)/(h)=15\text{ dollar per hour}`

Finally, solve for d( amount)

`\begin{gathered} (d)/(h)=15\text{ } \\ Multiply\text{ both sides by h} \\ (d)/(h)\cdot h=15\cdot h \\ d=15h \end{gathered}`

so, the answer is

B: d=15h