Question

The dollar amount d that Julia earns varies directly as the number of hours t that she works,and d=$116.25 when t=15h find t when d =$178.25

Answer 1

The given information is the dollars Julia earns varies directly as the number of hours she works.

Also, d=$116.25 when t=15 h.

The formula for the direct variation is:

`d=k\cdot t`

Where k is the constant of variation.

Replace the known values and find k:

`\begin{gathered} 116.25=k\cdot15 \\ k=(116.25)/(15) \\ k=7.75 \end{gathered}`

Now, to find t when d=178.25, replace d and k and solve for t in the direct variation equation:

`\begin{gathered} 178.25=7.75\cdot t \\ t=(178.25)/(7.75)^{} \\ t=23\text{ hours} \end{gathered}`

The answer is t=23 hours