Roger's Electronics Sells A Variety Of Computers And Other E
Roger's Electronics seils a variety of computers and other electronic
Roger's Electronics sells a variety of computers and other electronic devices. During the month of July, Roger's sold the following numbers of computers: Dates Total computers sold July 1-4 68 July Part A: Assuming that the proportional relationship between computers sold and days continues, write an equation that shows the amount of computers (y) sold per day (X) in July. Part B: How many computers were sold during the entire month of July (31 days long)?
Paper For Above instruction
The given problem involves understanding the relationship between the number of computers sold and the days in July, and then extending this understanding to calculate total sales for the entire month. The problem can be broken down into two parts: establishing a proportional relationship and applying it for total monthly sales.
Part A: Establishing the proportional relationship
Given that Roger's Electronics sold 68 computers during the first 4 days of July, we are asked to assume a proportional relationship between the number of computers sold and the number of days. This indicates that the number of computers sold per day remains constant, and the total sales over a period are directly proportional to the number of days.
To find the daily sales rate (y), we set up a proportional relationship. Let X represent the number of days, and y represent the total computers sold over those days. The data given is: over 4 days, 68 computers were sold.
Therefore, the daily sales rate (computers per day) can be calculated as:
Rate per day = total computers sold / number of days
Substituting the known values:
Rate per day = 68 / 4 = 17 computers per day
Since the sales are proportional to days, the mathematical equation that relates the total number of computers sold (y) to the number of days (X) is:
y = 17X
This equation indicates that for any number of days X in July, the total computers sold y can be obtained by multiplying the number of days by 17.
Part B: Calculating total sales in July (31 days)
Using the established equation y = 17X, we can now determine the total number of computers sold during the entire month of July, which has 31 days.
Substituting X = 31 into the equation:
y = 17 × 31 = 527
Hence, Roger's Electronics sold approximately 527 computers during the entire month of July.
This calculation is based on the assumption that the rate of sales remained consistent throughout July. It also presumes no fluctuations or special events that could have affected the sales volume during different periods of the month.
In real-world scenarios, sales might fluctuate due to various factors such as promotions, stock availability, or seasonal trends. However, based on the proportionality assumption provided, the total sales can be reliably estimated using this method.
In conclusion, the mathematical model y = 17X effectively captures the relationship between days and computers sold, providing a straightforward way to project sales based on initial data. The total estimated sales for July are approximately 527 computers, demonstrating the utility of proportional reasoning in sales forecasting.
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