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.
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.
