Answer :
To solve this problem, we need to find the average return rate for the laptop computers over the past six months and then use this rate to estimate the number of laptops sold in April based on the number of returns.
### Step-by-Step Solution:
1. Determine the return rate for each month:
The return rate is calculated as the number of returned laptops divided by the number of laptops sold for each month.
For October:
[tex]\[ \text{Return Rate (Oct)} = \frac{223}{1621} \approx 0.1376 \][/tex]
For November:
[tex]\[ \text{Return Rate (Nov)} = \frac{415}{1752} \approx 0.2369 \][/tex]
For December:
[tex]\[ \text{Return Rate (Dec)} = \frac{421}{1848} \approx 0.2278 \][/tex]
For January:
[tex]\[ \text{Return Rate (Jan)} = \frac{560}{1634} \approx 0.3427 \][/tex]
For February:
[tex]\[ \text{Return Rate (Feb)} = \frac{330}{1725} \approx 0.1913 \][/tex]
For March:
[tex]\[ \text{Return Rate (Mar)} = \frac{304}{1780} \approx 0.1708 \][/tex]
2. Calculate the average return rate:
The average return rate is the sum of the return rates for each month divided by the number of months.
[tex]\[ \text{Average Return Rate} = \frac{0.1376 + 0.2369 + 0.2278 + 0.3427 + 0.1913 + 0.1708}{6} \approx 0.2178 \][/tex]
3. Estimate the number of laptops sold in April:
Given that 379 laptops were returned in April, we can estimate the number of laptops sold using the average return rate.
[tex]\[ \text{Number of Laptops Sold (April)} = \frac{379}{0.2178} \approx 1739.78 \][/tex]
Rounding to the nearest integer, we get approximately 1,740 laptops.
Therefore, the most likely number of laptops sold in April is:
b. 1,740
### Step-by-Step Solution:
1. Determine the return rate for each month:
The return rate is calculated as the number of returned laptops divided by the number of laptops sold for each month.
For October:
[tex]\[ \text{Return Rate (Oct)} = \frac{223}{1621} \approx 0.1376 \][/tex]
For November:
[tex]\[ \text{Return Rate (Nov)} = \frac{415}{1752} \approx 0.2369 \][/tex]
For December:
[tex]\[ \text{Return Rate (Dec)} = \frac{421}{1848} \approx 0.2278 \][/tex]
For January:
[tex]\[ \text{Return Rate (Jan)} = \frac{560}{1634} \approx 0.3427 \][/tex]
For February:
[tex]\[ \text{Return Rate (Feb)} = \frac{330}{1725} \approx 0.1913 \][/tex]
For March:
[tex]\[ \text{Return Rate (Mar)} = \frac{304}{1780} \approx 0.1708 \][/tex]
2. Calculate the average return rate:
The average return rate is the sum of the return rates for each month divided by the number of months.
[tex]\[ \text{Average Return Rate} = \frac{0.1376 + 0.2369 + 0.2278 + 0.3427 + 0.1913 + 0.1708}{6} \approx 0.2178 \][/tex]
3. Estimate the number of laptops sold in April:
Given that 379 laptops were returned in April, we can estimate the number of laptops sold using the average return rate.
[tex]\[ \text{Number of Laptops Sold (April)} = \frac{379}{0.2178} \approx 1739.78 \][/tex]
Rounding to the nearest integer, we get approximately 1,740 laptops.
Therefore, the most likely number of laptops sold in April is:
b. 1,740
