Sure, let's solve this step-by-step.
Given:
- The number of girls in the class: 18
- The ratio of the number of girls to boys is [tex]\( 3:2 \)[/tex]
To find the number of boys, we need to use the ratio provided.
The ratio [tex]\( 3:2 \)[/tex] tells us that for every 3 parts (or units) of girls, there are 2 parts (or units) of boys. We can set up a proportion to find the number of boys.
Let's denote the number of boys by [tex]\( b \)[/tex].
The ratio of girls to boys can be written in the form of fractions:
[tex]\[ \frac{\text{girls}}{\text{boys}} = \frac{3}{2} \][/tex]
Since we know the number of girls is 18, we can substitute this into the proportion:
[tex]\[ \frac{18}{b} = \frac{3}{2} \][/tex]
We can solve for [tex]\( b \)[/tex] by cross-multiplying:
[tex]\[ 18 \times 2 = 3 \times b \][/tex]
[tex]\[ 36 = 3b \][/tex]
Now, we can solve for [tex]\( b \)[/tex] by dividing both sides of the equation by 3:
[tex]\[ b = \frac{36}{3} \][/tex]
[tex]\[ b = 12 \][/tex]
Therefore, the number of boys in the class is [tex]\( 12 \)[/tex].
