Cost of lectures = $7.33 per hour
Let [tex]e[/tex] the cost of the exam hours
Let [tex]w[/tex] be the cost of the workshop hours
Let [tex]l[/tex] be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
[tex]e=2w[/tex] equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
[tex]w=2l[/tex] equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
[tex]3e+24w+12l=528[/tex] equation (1)
Now, lets find the value of [tex]l[/tex]:
Step 1. Solve for [tex]l[/tex] in equation (3)
[tex]3e+24w+12l=528[/tex]
[tex]12l=528-3e-24w[/tex] equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
[tex]12l=528-3e-24w[/tex]
[tex]12l=528-3(2w)-24w[/tex]
[tex]12l=528-6w-24w[/tex]
[tex]12l=528-30w[/tex] equation (5)
Step 3. Replace equation (2) in equation (5) and solve for [tex]l[/tex]
[tex]12l=528-30w[/tex]
[tex]12l=528-30(2l)[/tex]
[tex]12l=528-60l[/tex]
[tex]72l=528[/tex]
[tex]l=\frac{528}{72}[/tex]
[tex]l=\frac{22}{3}[/tex]
[tex]l=7.33[/tex]
Cost of lectures = $7.33 per hour
