a karate studio charges $35 for the first course and $22.50 for each course after that, even if the student…

Explanation:

Step1: Subtract first - course fee

Let the number of courses after the first one be $x$. First, subtract the cost of the first course from the total amount paid. The amount paid for courses after the first one is $170 - 35=135$.

Step2: Calculate number of additional courses

Since each additional course costs $22.50$, we can find the number of additional courses $x$ by dividing the remaining amount by the cost per additional course. So $x=\frac{135}{22.5}=6$.

Step3: Calculate total number of courses

The total number of courses $n$ is the first course plus the number of additional courses. So $n = 1+x=1 + 6=7$.

Answer:

7 courses