<h2>Answer</h2>
Cost of lectures = $7.33 per hour
<h2>Explanation</h2>
Let
the cost of the exam hours
Let
be the cost of the workshop hours
Let
be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
equation (1)
Now, lets find the value of
:
Step 1. Solve for
in equation (3)
![3e+24w+12l=528](https://tex.z-dn.net/?f=3e%2B24w%2B12l%3D528)
equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
![12l=528-3e-24w](https://tex.z-dn.net/?f=12l%3D528-3e-24w)
![12l=528-3(2w)-24w](https://tex.z-dn.net/?f=12l%3D528-3%282w%29-24w)
![12l=528-6w-24w](https://tex.z-dn.net/?f=12l%3D528-6w-24w)
equation (5)
Step 3. Replace equation (2) in equation (5) and solve for ![l](https://tex.z-dn.net/?f=l)
![12l=528-30w](https://tex.z-dn.net/?f=12l%3D528-30w)
![12l=528-30(2l)](https://tex.z-dn.net/?f=12l%3D528-30%282l%29)
![12l=528-60l](https://tex.z-dn.net/?f=12l%3D528-60l)
![72l=528](https://tex.z-dn.net/?f=72l%3D528)
![l=\frac{528}{72}](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B528%7D%7B72%7D)
![l=\frac{22}{3}](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B22%7D%7B3%7D)
![l=7.33](https://tex.z-dn.net/?f=l%3D7.33)
Cost of lectures = $7.33 per hour