To solve this problem, we'll assign variables to the number of boys and girls in each class and use the information provided to form equations. Here's how we can approach it:

Define Variables

• Let $A_b$ and $A_g$ be the number of boys and girls in Class A, respectively.
• Let $B_b$ and $B_g$ be the number of boys and girls in Class B, respectively.
• Let $C_b$ and $C_g$ be the number of boys and girls in Class C, respectively.
• Let $D_b$ and $D_g$ be the number of boys and girls in Class D, respectively.
• Let $E_b$ and $E_g$ be the number of boys and girls in Class E, respectively.

Given Information and Forming Equations

1. Class D: Ratio of boys to girls is 11:7: $\frac{D_b}{D_g} = \frac{11}{7} \quad \Rightarrow \quad D_b = \frac{11}{7} D_g$

2. Number of girls in Class A is double the number of boys in Class B: $A_g = 2B_b$

3. Class C: Ratio of boys to girls is 15:8: $\frac{C_b}{C_g} = \frac{15}{8} \quad \Rightarrow \quad C_b = \frac{15}{8} C_g$

4. Number of boys in Class A is 21 less than the number of boys in Class D: $A_b = D_b - 21$

5. Total number of students in Class A is 65: $A_b + A_g = 65$

6. Total number of students in Class A is one less than the total number of boys in Classes B and C together: [ A_b + A_g + 1 = B_b + C_b