Question

there are 300 seniors tis year in the high school. of thus class, 140 take a math course and the 145 take a language course. if a student from the seniors that takes a math or a language course is 75% about how many from the seniors take both a math and a language course

Answer 1

Let \( M \) be the number of students taking a math course, \( L \) be the number of students taking a language course, and \( B \) be the number of students taking both courses.

From the problem, we know:

- Total seniors \( = 300 \)
- Students taking math \( M = 140 \)
- Students taking language \( L = 145 \)
- Students taking either math or language \( = 75\% \) of total seniors = \( 0.75 \times 300 = 225 \)

Using the principle of inclusion-exclusion for the number of students taking either a math or language course, we have:

\[
M + L - B = \text{number of students taking either course}
\]

Substituting in the known values gives us:

\[
140 + 145 - B = 225
\]

Now, simplifying that equation:

\[
285 - B = 225
\]

Solving for \( B \):

\[
B = 285 - 225
\]
\[
B = 60
\]

Thus, the number of students taking both a math and a language course is \( \boxed{60} \).