Since the income varies directly as the number of hours worked, we can write the following rule of three to calculate the income for 38 hours:
[tex]\begin{gathered} \text{hours}\to\text{income} \\ 8\text{ hours}\to336 \\ 38\text{ hours}\to x \end{gathered}[/tex]Now, let's write the following proportion and solve for x:
[tex]\begin{gathered} \frac{8}{38}=\frac{336}{x} \\ x\cdot8=336\cdot38 \\ x=\frac{336\cdot38}{8} \\ x=1596 \end{gathered}[/tex]Therefore the income for 38 hours is $1,596.
