Question

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?

Answer 1

Cost of lectures = $7.33 per hour

Step-by-step explanation

Let
`e` the cost of the exam hours

Let
`w` be the cost of the workshop hours

Let
`l` be the cost of the lecture hours.

We know from our problem that exam hours cost twice as much as workshop, so:

`e=2w` equation (1)

We also know that workshop hours cost twice as much as lecture hours, so:

`w=2l` equation (2)

Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:

`3e+24w+12l=528` equation (1)

Now, lets find the value of
`l`:

Step 1. Solve for
`l` in equation (3)

`3e+24w+12l=528`

`12l=528-3e-24w` equation (4)

Step 2. Replace equation (1) in equation (4) and simplify

`12l=528-3e-24w`

`12l=528-3(2w)-24w`

`12l=528-6w-24w`

`12l=528-30w` equation (5)

Step 3. Replace equation (2) in equation (5) and solve for
`l`

`12l=528-30w`

`12l=528-30(2l)`

`12l=528-60l`

`72l=528`

`l=(528)/(72)`

`l=(22)/(3)`

`l=7.33`

Cost of lectures = $7.33 per hour