Let's carefully step through solving the problem:
1. Identify the Information: We are given a table with the number of boys and girls who listen to Country Music and Rap Music. Here is the relevant information extracted from the table:
- Boys who listen to Country Music: 30 boys
- Boys who listen to Rap Music: 90 boys
2. Total Number of Boys:
To find the total number of boys, we need to sum the boys who listen to both genres:
[tex]\[
\text{Total boys} = \text{Boys who listen to Country Music} + \text{Boys who listen to Rap Music}
\][/tex]
Plugging in the values:
[tex]\[
\text{Total boys} = 30 + 90 = 120
\][/tex]
3. Number of Boys who Listen to Rap Music:
From the given data, we know:
[tex]\[
\text{Boys who listen to Rap Music} = 90
\][/tex]
4. Ratio of Boys who Listen to Rap Music to the Total Number of Boys:
Now, we need to find the ratio of boys who listen to Rap Music to the total number of boys.
This can be formulated as:
[tex]\[
\text{Ratio} = \frac{\text{Boys who listen to Rap Music}}{\text{Total boys}}
\][/tex]
Substituting the values:
[tex]\[
\text{Ratio} = \frac{90}{120}
\][/tex]
5. Simplify the Ratio:
Simplifying the fraction [tex]\(\frac{90}{120}\)[/tex] to its lowest terms involves finding the greatest common divisor (GCD) of 90 and 120. The GCD of 90 and 120 is 30.
Dividing both the numerator and the denominator by their GCD:
[tex]\[
\frac{90 \div 30}{120 \div 30} = \frac{3}{4}
\][/tex]
So, the ratio of boys who listen to Rap Music to the total number of boys, in its simplest form, is [tex]\(\frac{3}{4}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{\frac{3}{4}}\)[/tex].
