Respuesta :
Given that a retailer needs to purchase 12 printers, the first printer cost $54.
It is known that each additional printer costs 5% less than than the cost of the previous printer.
[tex]\text{Cost of first printer = \$54}[/tex]Cost of the second printer
The second printer costs 5% less than the first printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the second printer = }\frac{\text{5}}{100}\times54=2.7 \\ \text{Thus the price of the second printer =54-2.7=51.3} \end{gathered}[/tex]Cost of the third printer
The third printer costs 5% less than the second printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the third printer = }\frac{\text{5}}{100}\times51.3=2.565 \\ \text{Thus the price of the third printer =51.3-2.565=}48.735 \end{gathered}[/tex]Cost of the fourth printer
The fourth printer costs 5% less than the third printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the fourth printer = }\frac{\text{5}}{100}\times48.735=2.437 \\ \text{Thus the price of the fourth printer =48.735-2.437=}46.298 \end{gathered}[/tex]Cost of the fifth printer
The fifth printer costs 5% less than the fourth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the fifth printer = }\frac{\text{5}}{100}\times46.298=2.315 \\ \text{Thus the price of the fifth printer =46.298-2.315=}43.981 \end{gathered}[/tex]Cost of the sixth printer
The sixth printer costs 5% less than the fifth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the sixth printer = }\frac{\text{5}}{100}\times43.981=2.199 \\ \text{Thus the price of the sixth printer =43.981-2.199=}41.782 \end{gathered}[/tex]Cost of the seventh printer
The seventh printer costs 5% less than the sixth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the seventh printer = }\frac{\text{5}}{100}\times41.782=2.089 \\ \text{Thus, the price of the seventh printer =41.782-2.089=}39.693 \end{gathered}[/tex]Cost of the eighth printer
The eighth printer costs 5% less than the seventh printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the eighth printer = }\frac{\text{5}}{100}\times39.693=1.985 \\ \text{Thus, the price of the eighth printer =39.693-1.985=}37.708 \end{gathered}[/tex]Cost of the ninth printer
The ninth printer costs 5% less than the eighth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the ninth printer = }\frac{\text{5}}{100}\times37.708=1.885 \\ \text{Thus, the price of the ninth printer =37.708-1.885=}35.823 \end{gathered}[/tex]Cost of the tenth printer
The tenth printer costs 5% less than the ninth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the tenth printer = }\frac{\text{5}}{100}\times35.823=1.791 \\ \text{Thus, the price of the tenth printer =35.823-1.791=}34.032 \end{gathered}[/tex]Cost of the eleventh printer
The eleventh printer costs 5% less than the tenth printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the eleventh printer = }\frac{\text{5}}{100}\times34.032=1.702 \\ \text{Thus, the price of the eleventh printer =34.032-1.702=}32.33 \end{gathered}[/tex]Cost of the twelfth printer
The twelfth printer costs 5% less than the eleventh printer, we thus have
[tex]\begin{gathered} D\text{iscount price on the twelfth printer = }\frac{\text{5}}{100}\times32.33=1.617 \\ \text{Thus, the price of the twelfth printer =32.33-1.617=}30.713 \end{gathered}[/tex]Thus, the total cost of 12 printers is evaluated as
[tex]\begin{gathered} 54+51.3+48.735+46.298+43.981+41.782+39.693+37.708+35.823+34.032+32.33+30.713_{_{_{}}} \\ =496.4 \end{gathered}[/tex]Thus, the sum of twelve printers is $496.4
The second option is the correct answer.
