Let's solve this problem step-by-step by analyzing the given information and forming an equation to find the required percentage of blue cell phones sold.
Given the table:
[tex]\[
\begin{array}{|l|l|}
\hline \text{Color} & \begin{array}{c}
\text{Percentage of Cell} \\
\text{Phones Sold}
\end{array} \\
\hline \text{White} & 8k \\
\hline \text{Black} & 30 \\
\hline \text{Blue} & 30 - 2k \\
\hline \text{Red} & k + 5 \\
\hline \text{Total} & 100 \\
\hline
\end{array}
\][/tex]
We are given that the total percentage of cell phones sold is 100%. From the table, we can sum up the percentages of each color to form an equation:
[tex]\[
8k + 30 + (30 - 2k) + (k + 5) = 100
\][/tex]
Let's simplify and solve this equation:
1. First, combine the like terms:
[tex]\[
8k + 30 + 30 - 2k + k + 5 = 100
\][/tex]
[tex]\[
(8k - 2k + k) + (30 + 30 + 5) = 100
\][/tex]
[tex]\[
7k + 65 = 100
\][/tex]
2. Next, isolate [tex]\(k\)[/tex] by moving the constant term to the other side of the equation:
[tex]\[
7k + 65 - 65 = 100 - 65
\][/tex]
[tex]\[
7k = 35
\][/tex]
3. Solve for [tex]\(k\)[/tex] by dividing both sides by 7:
[tex]\[
k = \frac{35}{7}
\][/tex]
[tex]\[
k = 5
\][/tex]
Now that we have the value of [tex]\(k\)[/tex], we need to determine the percentage of blue cell phones sold, given by the expression [tex]\(30 - 2k\)[/tex]:
[tex]\[
30 - 2k = 30 - 2(5)
\][/tex]
[tex]\[
30 - 10 = 20
\][/tex]
Thus, the percentage of blue cell phones sold is:
[tex]\[
\boxed{20\%}
\][/tex]
Therefore, the correct answer is:
B. 20%
