The number of girls in Stephen's class exceeded the number of boys by $8$ . If there were $36$ pupils in the class, how many were girls and how many were boys?

Full solution

Q. The number of girls in Stephen's class exceeded the number of boys by

8

. If there were

36

pupils in the class, how many were girls and how many were boys?

Equation $1$ : Let's denote the number of boys as $B$ and the number of girls as $G$ . According to the problem, the number of girls exceeded the number of boys by $8$ , so we can write the following equation: $\newline$ $G = B + 8$
Equation $2$ : We also know that the total number of pupils in the class is $36$ . This gives us a second equation: $\newline$ $G + B = 36$
Substitute and Solve: Now we have a system of two equations with two variables: $\newline$ $1$ ) $G = B + 8$ $\newline$ $2$ ) $G + B = 36$ $\newline$ We can substitute the expression for $G$ from the first equation into the second equation to find the value of $B$ . $\newline$ $(B + 8) + B = 36$
Find Boys: Solving for $B$ , we combine like terms: $\newline$ $2B + 8 = 36$ $\newline$ $2B = 36 - 8$ $\newline$ $2B = 28$ $\newline$ $B = \frac{28}{2}$ $\newline$ $B = 14$ $\newline$ So, there are $14$ boys in the class.
Find Girls: Now that we know the number of boys, we can find the number of girls using the first equation: $\newline$ $G = B + 8$ $\newline$ $G = 14 + 8$ $\newline$ $G = 22$ $\newline$ So, there are $22$ girls in the class.