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?

Summary Submit Skip Question

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 $s$ :

$$\boxed{f(s)=125(20-s)+155s}$$