Question

1. There are 78 sophomores at a school. Each is required to take at least one year of either chemistry or physics, but they may take both. 15 are enrolled in both chemistry and phys- ics, and 47 are enrolled only in chemistry. How many students are enrolled only in physics?

Answer 1

We are given that there are a total of 78 students. If we set the following variables:

$\begin{gathered} C=\text{students only in chemestry} \\ P=\text{students only in physics} \\ PC=\text{students in physics and chemistry} \end{gathered}$

Then, the sum of all of these must be 78, that is:

$C+P+PC=78$

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

$47+P+15=78$

Simplifying:

$62+P=78$

Now we solve for P by subtracting 62 on both sides:

$\begin{gathered} 62-62+P=78-62 \\ P=16 \end{gathered}$

Therefore, there are 16 students in physics