CELL PHONE SALES BY COLOR

[tex]\[
\begin{tabular}{|l|l|}
\hline
Color & \multicolumn{1}{|c|}{\begin{tabular}{c}
Percentage of Cell \\
Phones Sold
\end{tabular}} \\
\hline
White & $8k$ \\
\hline
Black & 30 \\
\hline
Blue & $30-2k$ \\
\hline
Red & $k+5$ \\
\hline
Total & 100 \\
\hline
\end{tabular}
\][/tex]

The table above shows cell phone sales by color. What percentage of the cell phones sold were blue?

A. [tex]$18\%$[/tex]
B. [tex]$20\%$[/tex]
C. [tex]$22\%$[/tex]
D. [tex]$28\%$[/tex]



Answer :

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%