To find the number of girls and boys in the class, let's denote the number of girls as [tex]\( G \)[/tex] and the number of boys as [tex]\( B \)[/tex]. According to the problem, the class has a total of 64 students, and the number of boys is [tex]\(\frac{3}{5}\)[/tex] of the number of girls.
We start by setting up the equation based on the given relationships:
1. The total number of students is 64:
[tex]\[
G + B = 64
\][/tex]
2. The number of boys is [tex]\(\frac{3}{5}\)[/tex] of the number of girls:
[tex]\[
B = \frac{3}{5}G
\][/tex]
Next, substitute the expression for [tex]\( B \)[/tex] from the second equation into the first equation:
[tex]\[
G + \frac{3}{5}G = 64
\][/tex]
To combine the terms involving [tex]\( G \)[/tex], convert the fraction to a common denominator if necessary. Here, we can simply add the coefficients:
[tex]\[
\left(1 + \frac{3}{5}\right)G = 64
\][/tex]
Convert 1 to a fraction with a denominator of 5:
[tex]\[
\left(\frac{5}{5} + \frac{3}{5}\right)G = 64
\][/tex]
[tex]\[
\frac{8}{5}G = 64
\][/tex]
To solve for [tex]\( G \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{8}{5}\)[/tex]:
[tex]\[
G = 64 \times \frac{5}{8}
\][/tex]
[tex]\[
G = 40
\][/tex]
Therefore, the number of girls [tex]\( G \)[/tex] is 40.
Next, we calculate the number of boys [tex]\( B \)[/tex] using the relationship [tex]\( B = \frac{3}{5}G \)[/tex]:
[tex]\[
B = \frac{3}{5} \times 40
\][/tex]
[tex]\[
B = 24
\][/tex]
Therefore, the number of boys [tex]\( B \)[/tex] is 24.
In summary, the class consists of 40 girls and 24 boys.
