Answer :
To solve the problem of finding how many boys were in the group of 25 grade 7 learners watching a soccer match given the ratio of boys to girls is 2:3, we need to follow these steps:
Understand the Ratio: The problem tells us that the ratio of the number of boys to the number of girls is 2:3. This means for every 2 boys, there are 3 girls.
Use the Ratio to Create an Equation: Let the number of boys be [tex]2x[/tex] and the number of girls be [tex]3x[/tex]. The sum of boys and girls is 25, as per the problem statement.
Set Up the Equation: We can add the expressions for boys and girls to equal the total number of learners:
[tex]2x + 3x = 25[/tex]
Solve the Equation: Combine like terms:
[tex]5x = 25[/tex]
Solve for [tex]x[/tex] by dividing both sides by 5:
[tex]x = \frac{25}{5} = 5[/tex]
Find the Number of Boys: Since [tex]x = 5[/tex], substitute back into the expression for boys:
[tex]2x = 2(5) = 10[/tex]
Conclusion: There are 10 boys in the group of grade 7 learners.
By understanding and applying the concept of ratios, we've determined that out of the 25 learners, 10 were boys.
