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].
