To complete this two-way table, we need to fill in the missing values using the information given in the rows and columns. Here’s how to solve it step-by-step:

Step 1: Determine Missing Values in Grade 7 Row

1. Add up the entries in the "Arabic" and "Total" columns for Grade 7:

   • The total for Grade 7 is 45.
   • Grade 7 Arabic students are 11.

   To find the number of students studying Spanish and Mandarin in Grade 7, subtract 11 from 45: $45 - 11 = 34$

   Now, 34 students are studying either Spanish or Mandarin in Grade 7.

2. Use the column totals to find Grade 7 Spanish students:

   • The total number of students studying Spanish is 37, and Grade 8 Spanish students are 19.

   To find the Grade 7 Spanish students: $37 - 19 = 18$

   So, 18 Grade 7 students study Spanish.

3. Calculate Grade 7 Mandarin students:

   • Since we found 34 students studying either Spanish or Mandarin, and 18 of them study Spanish, the remaining are studying Mandarin: $34 - 18 = 16$

   Thus, 16 Grade 7 students study Mandarin.

Step 2: Determine Missing Values in Grade 8 Row

4. Calculate Grade 8 Mandarin students:

   • The total number of Mandarin students is 50.
   • Grade 7 has 16 Mandarin students.

   So, Grade 8 Mandarin students: $50 - 16 = 34$

5. Calculate Total for Grade 8 Row:

   • Sum the Grade 8 values for each language: $19 \text{ (Spanish)} + 34 \text{ (Mandarin)} + 26 \text{ (Arabic)} = 79$

Now, the table is completed as follows: