in one school 65 students speak Spanish and 49 speak Japanese if 80 students speak either Spanish or Japanese how many states speak both Spanish and Japanese

Answer 1

To find out how many students speak both Spanish and Japanese, we can use the principle of inclusion-exclusion.

Let:

• \( S \) be the number of students who speak Spanish, which is 65.
• \( J \) be the number of students who speak Japanese, which is 49.
• \( U \) be the total number of students who speak either Spanish or Japanese, which is 80.
• \( B \) be the number of students who speak both languages.

Using the formula for the union of two sets, we have:

\[ U = S + J - B \]

Substituting the known values into the equation:

\[ 80 = 65 + 49 - B \]

Now, combine the numbers:

\[ 80 = 114 - B \]

Solving for \( B \):

\[ B = 114 - 80 \]

\[ B = 34 \]

Therefore, the number of students who speak both Spanish and Japanese is 34.