Answer:
2 classes at Hilltop, 3 classes at Serra; and $20,600
Explanation:
We can generate two equations from the problem
Equation 1: Dr. Lum can teach up to 5 classes per semester at both colleges. If 'h' represents the number of classes taken at Hilltop College, and 's', the number of classes taken at Serra College,
<em>Equation 1 becomes: h + s = 5</em>
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Equation 2: Dr. Lum spends 3 hours per week preparing for Hilltop classes, and 4 hours for Serra classes, subject to a maximum of 18 hours per week.
<em>Equation 2 becomes: 3h + 4s = 18</em>
Now solving using substitution method,
We can derive an equation 3 from equation 1, as follows.
<em>Equation 3: h = 5 - s.</em>
Substituting equation 3 into equation 2, equation 2 becomes
3(5 - s) + 4s = 18
= 15 - 3s + 4s = 18
= 15 + s = 18
= s = 3.
With s = 3, using equation 3, h = 5 - 3 = 2.
Therefore, Dr. Lum should teach 2 classes at Hilltop, and 3 classes at Serra.
His income will be
$4,000 (2) + $4,200 (3)
= $20,600.
