Question

At the north campus of a performing arts​ school, ​20% of the students are music majors. At the south​ campus, 70​% of the students are music majors. The campuses are merged into one east campus. If ​30% of the 1000 students at the east campus are music​ majors, how many students did the north and south campuses have before the​ merger?

Answer 1

Answer:

The north campus had $800$ while the south campus had $200$.

Step-by-step explanation:

The question stated that there are $1000$ students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.

Let $x$ denote the number of students in the north campus before the merger. The other $(1000 -x)$ students would all belong to the south campus before the merger.

Before the merger, $20\%$ of the students of the north campus are of music majors. In terms of $x$, that's $(20\%)\cdot x = 0.20\,x$ students.

On the other hand, $70\%$ of the students of the south campus are of music majors. That corresponds to $(70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x$ students.

With a similar logic, the number of music students in the merged east campus will be $30\% \times 1000 = 300$.

The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:

$0.20\, x+ (700 - 0.70\, x) = 300$.

Solve for $x$:

$x = 800$.

In other words, there are $800$ students in the north campus and $(1000 - 800) = 200$ students in the south campus before the merger.