Question

A retailer needs to purchase 10 printers. The first printer costs $57, and each additional printer costs 3% less than the price of the previous printer, up to 15 printers. What is the total cost of 10 printers?(did not mean to select an answer)

Answer 1

Solution

- The solution steps are given below:

$\begin{gathered} \text{ The sum of the costs is given as:} \\ 57+(1-0.03)(57)+(1-0.03)((1-0.03)(57))+... \\ 57+0.97(57)+0.97(0.97(57))+... \\ 57+0.97(57)+0.97^2(57)+... \\ \\ \text{ The sum is a geometric series such that:} \\ r=0.97 \\ a=57 \\ \\ \text{ Therefore, we can find the sum using the formula for the sum of a geometric series.} \\ S_n=\frac{a(1-r^n)}{1-r} \\ \\ n=10,\text{ from the question} \\ \\ \\ S_{10}=\frac{57(1-0.97^{10})}{1-0.97} \\ \\ S_{10}=498.8941...\approx498.89 \end{gathered}$

Final Answer

The answer is $498.89