Sure, let's solve the problem step-by-step.
Given:
- There are 18 girls in a class.
- The ratio of the number of boys to the number of girls in the class is 4:3.
a) According to the given ratio, we need to find who are in greater number, boys or girls.
Step 1: Define the ratio.
The ratio of boys to girls is 4:3. This can be written as:
[tex]\[ \text{Ratio} = \frac{\text{Number of boys}}{\text{Number of girls}} = \frac{4}{3} \][/tex]
Step 2: Set up the equation.
Let's denote the number of boys as [tex]\( b \)[/tex] and the number of girls as [tex]\( g \)[/tex].
Given [tex]\( g = 18 \)[/tex] (as there are 18 girls in the class), we can use the ratio to set up the equation:
[tex]\[ \frac{b}{g} = \frac{4}{3} \][/tex]
Step 3: Substitute the number of girls into the equation.
[tex]\[ \frac{b}{18} = \frac{4}{3} \][/tex]
Step 4: Solve for the number of boys [tex]\( b \)[/tex].
To solve for [tex]\( b \)[/tex], we cross-multiply:
[tex]\[ 3b = 4 \times 18 \][/tex]
[tex]\[ 3b = 72 \][/tex]
[tex]\[ b = \frac{72}{3} \][/tex]
[tex]\[ b = 24 \][/tex]
So, the number of boys in the class is 24.
Step 5: Compare the numbers of boys and girls.
Now, we have:
- Number of girls [tex]\( g = 18 \)[/tex]
- Number of boys [tex]\( b = 24 \)[/tex]
Since [tex]\( 24 > 18 \)[/tex], the boys are in greater number.
Therefore, according to the given ratio, the number of boys is 24, and boys are in greater number in the class.
