For the level 3 course, exam hours cost twice as much as workshop hours, workshop hours cost twice as much as lecture hours. How much are lectures per hour?

AnswerCost of lectures = $7.33 per hourExplanationLet [tex]e[/tex] the cost of the exam hours Let [tex]w[/tex] be the cost of the workshop hoursLet [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