There are five classes: A, B, C, D and E. Each class has different numbers of boys and girls. The ratio of boys to girls in class D is 11:7 respectively. The number of girls in class A is double the number of boys in class B. The ratio of boys to girls in class C is 15:8 respectively. The number of boys in class A is 21 less than the number of boys in class D. The total number of students in class A is 65, which is one less than the number of boys in class B and C together. The ratio of the number of girls in class B and C is 13:8 respectively. The number of boys and girls in class E is equal. The ratio of the number of boys in class C and E is 15:11 respectively. The total number of girls in all classes together is 166.

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

Learn how to solve complex word problems involving ratios and equations with detailed step-by-step solutions. This problem covers various mathematical concepts including ratio relationships, equation formations, and total student calculation. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation