Questions: The sales of vinyl records have increased due to a revived popularity. In the year 2012, 50,000 records were sold. Every following year, the number of records sold were 1.1 times the number of records sold the previous year. From 2012 to the end of 2016, how many vinyl records were sold? A. 80,525 records B. 255,255 records C. 73,205 records D. 305,255 records

Solution Steps

In the year 2012, the initial number of vinyl records sold is given as \( 50000 \).

The sales for each subsequent year can be calculated using the formula: \[ \text{Sales}_{n} = \text{Sales}_{n-1} \times 1.1 \] where \( n \) represents the year. Thus, we calculate the sales for each year from 2012 to 2016 as follows:

• For 2013: \[ \text{Sales}_{2013} = 50000 \times 1.1 \]
• For 2014: \[ \text{Sales}_{2014} = \text{Sales}_{2013} \times 1.1 \]
• For 2015: \[ \text{Sales}_{2015} = \text{Sales}_{2014} \times 1.1 \]
• For 2016: \[ \text{Sales}_{2016} = \text{Sales}_{2015} \times 1.1 \]

To find the total number of records sold from 2012 to 2016, we sum the sales for each year: \[ \text{Total Sales} = \text{Sales}_{2012} + \text{Sales}_{2013} + \text{Sales}_{2014} + \text{Sales}_{2015} + \text{Sales}_{2016} \] Substituting the calculated values will yield the total sales over the specified period.

Final Answer