There are two schools A and B in a town. Let the total number of boys in school A be $X$ and the total number of girls in school A be $Y$. The total number of girls in school B is 30 more than twice the number of girls in school A. The total number of boys in school B is equal to the total number of students (boys + girls) in school A.

What is the expression for the difference between the total number of boys in both schools and the total number of girls in both schools?

Question

There are two schools A and B in a town. Let the total number of boys in school A be $X$ and the total number of girls in school A be $Y$. The total number of girls in school B is 30 more than twice the number of girls in school A. The total number of boys in school B is equal to the total number of students (boys + girls) in school A.

What is the expression for the difference between the total number of boys in both schools and the total number of girls in both schools?

Accepted Answer

**Solution:**

1. Let the number of boys in school A be $X$ and the number of girls in school A be $Y$.

2. According to the problem:
   - Total boys in school B = total students in school A = $X + Y$
   - Total girls in school B = $2Y + 30$

3. Total boys in both schools = boys in A + boys in B = $X + (X + Y) = 2X + Y$

4. Total girls in both schools = girls in A + girls in B = $Y + (2Y + 30) = 3Y + 30$

5. Required difference = (total boys in both schools) - (total girls in both schools)

$$= (2X + Y) - (3Y + 30) = 2X + Y - 3Y - 30 = 2X - 2Y - 30$$

**Answer:** $2X - 2Y - 30$

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