Answer :
First, let's define the sequence of operations and reverse apply them to determine the original price of the chair. The final price of the chair is given as $167.79. Below are the steps performed to find the original price:
1. Step 1: Reversing the 18% markdown:
The final price after this markdown was given as $167.79. To find the price before the markdown, divide by \(1 - 0.18 = 0.82\).
[tex]\[ \text{Price before 18\% markdown} = \frac{167.79}{0.82} = 204.62 \][/tex]
2. Step 2: Reversing the 40% markup:
The price just before the last markdown and after the 40% markup can be calculated by dividing by \(1 + 0.40 = 1.40\).
[tex]\[ \text{Price before 40\% markup} = \frac{204.62}{1.40} = 146.16 \][/tex]
3. Step 3: Reversing the 36% markdown:
The price just before the last markup and after the 36% markdown can be found by dividing by \(1 - 0.36 = 0.64\).
[tex]\[ \text{Price before 36\% markdown} = \frac{146.16}{0.64} = 228.37 \][/tex]
4. Step 4: Reversing the 30% markup:
The price just before the second markdown and after the 30% markup can be found by dividing by \(1 + 0.30 = 1.30\).
[tex]\[ \text{Price before 30\% markup} = \frac{228.37}{1.30} = 175.67 \][/tex]
5. Step 5: Reversing the 22% markup:
The original price before all the changes was the price just before the first markup and can be found by dividing by \(1 + 0.22 = 1.22\).
[tex]\[ \text{Original Price} = \frac{175.67}{1.22} = 143.99 \][/tex]
Therefore, after rounding to the nearest dollar, the original price of the desk chair is:
[tex]\[ \$144 \][/tex]
So, the best answer from the choices provided is:
c. \$144.
1. Step 1: Reversing the 18% markdown:
The final price after this markdown was given as $167.79. To find the price before the markdown, divide by \(1 - 0.18 = 0.82\).
[tex]\[ \text{Price before 18\% markdown} = \frac{167.79}{0.82} = 204.62 \][/tex]
2. Step 2: Reversing the 40% markup:
The price just before the last markdown and after the 40% markup can be calculated by dividing by \(1 + 0.40 = 1.40\).
[tex]\[ \text{Price before 40\% markup} = \frac{204.62}{1.40} = 146.16 \][/tex]
3. Step 3: Reversing the 36% markdown:
The price just before the last markup and after the 36% markdown can be found by dividing by \(1 - 0.36 = 0.64\).
[tex]\[ \text{Price before 36\% markdown} = \frac{146.16}{0.64} = 228.37 \][/tex]
4. Step 4: Reversing the 30% markup:
The price just before the second markdown and after the 30% markup can be found by dividing by \(1 + 0.30 = 1.30\).
[tex]\[ \text{Price before 30\% markup} = \frac{228.37}{1.30} = 175.67 \][/tex]
5. Step 5: Reversing the 22% markup:
The original price before all the changes was the price just before the first markup and can be found by dividing by \(1 + 0.22 = 1.22\).
[tex]\[ \text{Original Price} = \frac{175.67}{1.22} = 143.99 \][/tex]
Therefore, after rounding to the nearest dollar, the original price of the desk chair is:
[tex]\[ \$144 \][/tex]
So, the best answer from the choices provided is:
c. \$144.
