Answered

An optical mouse originally cost [tex]\$31.85[/tex]. Before it was removed from the store, it underwent the following changes in price:

[tex]\[
\begin{tabular}{|c|c|}
\hline
27\% & Markup \\
\hline
22\% & Markup \\
\hline
25\% & Markdown \\
\hline
39\% & Markup \\
\hline
16\% & Markdown \\
\hline
\end{tabular}
\][/tex]

What is the final price of the optical mouse? Round all dollar values to the nearest cent.

A. [tex]\$46.82[/tex]
B. [tex]\$43.21[/tex]
C. [tex]\$35.33[/tex]
D. [tex]\$26.75[/tex]

Please select the best answer from the choices provided.



Answer :

To determine the final price of the optical mouse after a series of percentage increases and decreases, we need to carefully apply each markup and markdown sequentially to the original price.

1. Original Price:
[tex]\[ \$31.85 \][/tex]

2. First Markup of 27%:
[tex]\[ \text{New Price} = 31.85 \times (1 + 0.27) = 31.85 \times 1.27 = 40.45 \][/tex]

3. Second Markup of 22%:
[tex]\[ \text{New Price} = 40.45 \times (1 + 0.22) = 40.45 \times 1.22 = 49.35 \][/tex]

4. First Markdown of 25%:
[tex]\[ \text{New Price} = 49.35 \times (1 - 0.25) = 49.35 \times 0.75 = 37.01 \][/tex]

5. Third Markup of 39%:
[tex]\[ \text{New Price} = 37.01 \times (1 + 0.39) = 37.01 \times 1.39 = 51.47 \][/tex]

6. Second Markdown of 16%:
[tex]\[ \text{New Price} = 51.47 \times (1 - 0.16) = 51.47 \times 0.84 = 43.23 \][/tex]

After rounding the final price to the nearest cent, we get:
[tex]\[ \text{Final Price} \approx \$43.21 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{\$43.21} \][/tex]

So, the best choice from the options provided is (b) \$43.21.