Solving the Classroom Ratio Puzzle: A Mathematical Exploration

Here's a brain-teasing math problem that involves ratios and algebra. The question is:

There are 5 more girls than boys in a class. If 2 boys join the class, the ratio of girls to boys will be 5:4. How many girls are in the class?

Step-by-Step Solution

To solve this problem, we can set up some algebraic equations based on the information provided. Let's denote the number of boys in the class as ( b ) and the number of girls as ( g ).

Setting Up the Equations

First, we are given that there are 5 more girls than boys:

( g b 5 )

If 2 more boys join the class, the new number of boys will be ( b 2 ), and the ratio of girls to boys becomes 5:4:

( frac{g}{b 2} frac{5}{4} )

Substituting and Solving for ( g )

Now, let's express the second equation in terms of ( g ) and ( b ):

( 4g 5(b 2) )

Substituting the first equation into this one:

( 4(b 5) 5(b 2) )

Expanding and simplifying:

( 4b 20 5b 10 )

Now, distribute and rearrange:

( 4b 20 5b 10 )

( 20 - 10 5b - 4b )

( 10 b )

Now that we have the number of boys, we can find the number of girls using the first equation:

( g b 5 10 5 15 )

Verification

Let's verify this solution:

Initially, there are 15 girls and 10 boys. If 2 boys join, there will be 12 boys. The new ratio is:

( frac{15}{12} frac{5}{4} )

Thus, the solution is correct.

Conclusion

The number of girls in the class is ( boxed{15} ).