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A floor lamp originally cost [tex]\$44.50[/tex]. Over a period of two months, it underwent the following changes in price:

\begin{tabular}{|c|c|}
\hline
[tex]$62\%$[/tex] & Markup \\
\hline
[tex]$15\%$[/tex] & Markdown \\
\hline
[tex]$18\%$[/tex] & Markup \\
\hline
[tex]$20\%$[/tex] & Markup \\
\hline
[tex]$45\%$[/tex] & Markdown \\
\hline
\end{tabular}

What is the final price of the floor lamp? Round all dollar values to the nearest cent.

A. [tex]\$62.30[/tex]
B. [tex]\$47.72[/tex]
C. [tex]\$35.60[/tex]
D. [tex]\$24.48[/tex]

Please select the best answer from the choices provided.



Answer :

GinnyAnswer
Let’s find the final price of the floor lamp step-by-step, taking into account each change in price:

1. Initial Price:
The initial price of the floor lamp is \(\$44.50\).

2. First Markup (62%):
[tex]\[ \text{Price after 62% markup} = 44.50 \times (1 + 0.62) = 44.50 \times 1.62 = 72.09 \][/tex]

3. First Markdown (15%):
[tex]\[ \text{Price after 15% markdown} = 72.09 \times (1 - 0.15) = 72.09 \times 0.85 = 61.28 \][/tex]
(Rounded to the nearest cent)

4. Second Markup (18%):
[tex]\[ \text{Price after 18% markup} = 61.28 \times (1 + 0.18) = 61.28 \times 1.18 = 72.31 \][/tex]
(Rounded to the nearest cent)

5. Third Markup (20%):
[tex]\[ \text{Price after 20% markup} = 72.31 \times (1 + 0.20) = 72.31 \times 1.20 = 86.77 \][/tex]
(Rounded to the nearest cent)

6. Second Markdown (45%):
[tex]\[ \text{Final price after 45% markdown} = 86.77 \times (1 - 0.45) = 86.77 \times 0.55 = 47.72 \][/tex]
(Rounded to the nearest cent)

Thus, after applying all the percentage changes in sequence, the final price of the floor lamp is \(\$47.72\).

Among the given choices, the correct answer is:

b. [tex]\(\$47.72\)[/tex].

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