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

Answer 1

Let's define the variables:

• Let \( A \) be the number of students taking a math course.
• Let \( B \) be the number of students taking a language course.
• Let \( X \) be the number of students taking both math and language courses.

We know that:

• \( A = 140 \)
• \( B = 145 \)
• The number of seniors taking either math or language (or both) is given as 75% of the total seniors. Therefore:

\[ \text{Number of seniors taking a math or language course} = 0.75 \times 300 = 225 \]

We can use the principle of inclusion-exclusion to express the total number of students taking at least one of the courses:

\[ A + B - X = \text{Number of seniors taking math or language course} \]

Substituting the values we have:

\[ 140 + 145 - X = 225 \]

Combining the numbers:

\[ 285 - X = 225 \]

Now we solve for \( X \):

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

Therefore, the number of seniors taking both a math and a language course is 60.