A substitute teacher in Southern California can expect to earn $125 per day. Sometimes, they can be put in long-term positions when a teacher is gone for longer periods of time.
For these periods, a substitute teacher earns $30 more than their regular rate. If Mike worked as a substitute teacher \(20\) days this past month and \(s\) of those days were classified as long-term, which
of the following functions gives the total amount, in dollars, Mike made last month?
We need to construct a model that gives the total amount. We can seperate the amount into regular days and long-term days.
$$ \text{ total pay}=\text{pay for regular days}+\text{pay for long-term days} $$
A teacher gets paid \(\$125+\$30=\$155\) per long-term day. Working \(s\) long-term days:
$$ \text{pay for long term-days} = 155 \cdot s $$
Since there are 20 days in total, the number of regular days must be \(20-s\). Similarly, at \(\$125\) per regular day,
$$ \text{pay for regular days}= 125 \cdot (20-s) $$
Putting this all together:
$$ \text{total pay}=155s+125(20-s) $$
Total pay as a function of \(s\) :
$$ \boxed{f(s)=125(20-s)+155s}$$