Question

A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers? $368.58 $496.41 $615.60 $618.30

Answer 1

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.

`\text{Cost of first printer = \$54}`

Cost of the second printer

The second printer costs 5% less than the first printer, we thus have

`\begin{gathered} D\text{iscount price on the second printer = }\frac{\text{5}}{100}*54=2.7 \\ \text{Thus the price of the second printer =54-2.7=51.3} \end{gathered}`

Cost of the third printer

The third printer costs 5% less than the second printer, we thus have

`\begin{gathered} D\text{iscount price on the third printer = }\frac{\text{5}}{100}*51.3=2.565 \\ \text{Thus the price of the third printer =51.3-2.565=}48.735 \end{gathered}`

Cost of the fourth printer

The fourth printer costs 5% less than the third printer, we thus have

`\begin{gathered} D\text{iscount price on the fourth printer = }\frac{\text{5}}{100}*48.735=2.437 \\ \text{Thus the price of the fourth printer =48.735-2.437=}46.298 \end{gathered}`

Cost of the fifth printer

The fifth printer costs 5% less than the fourth printer, we thus have

`\begin{gathered} D\text{iscount price on the fifth printer = }\frac{\text{5}}{100}*46.298=2.315 \\ \text{Thus the price of the fifth printer =46.298-2.315=}43.981 \end{gathered}`

Cost of the sixth printer

The sixth printer costs 5% less than the fifth printer, we thus have

`\begin{gathered} D\text{iscount price on the sixth printer = }\frac{\text{5}}{100}*43.981=2.199 \\ \text{Thus the price of the sixth printer =43.981-2.199=}41.782 \end{gathered}`

Cost of the seventh printer

The seventh printer costs 5% less than the sixth printer, we thus have

`\begin{gathered} D\text{iscount price on the seventh printer = }\frac{\text{5}}{100}*41.782=2.089 \\ \text{Thus, the price of the seventh printer =41.782-2.089=}39.693 \end{gathered}`

Cost of the eighth printer

The eighth printer costs 5% less than the seventh printer, we thus have

`\begin{gathered} D\text{iscount price on the eighth printer = }\frac{\text{5}}{100}*39.693=1.985 \\ \text{Thus, the price of the eighth printer =39.693-1.985=}37.708 \end{gathered}`

Cost of the ninth printer

The ninth printer costs 5% less than the eighth printer, we thus have

`\begin{gathered} D\text{iscount price on the ninth printer = }\frac{\text{5}}{100}*37.708=1.885 \\ \text{Thus, the price of the ninth printer =37.708-1.885=}35.823 \end{gathered}`

Cost of the tenth printer

The tenth printer costs 5% less than the ninth printer, we thus have

`\begin{gathered} D\text{iscount price on the tenth printer = }\frac{\text{5}}{100}*35.823=1.791 \\ \text{Thus, the price of the tenth printer =35.823-1.791=}34.032 \end{gathered}`

Cost of the eleventh printer

The eleventh printer costs 5% less than the tenth printer, we thus have

`\begin{gathered} D\text{iscount price on the eleventh printer = }\frac{\text{5}}{100}*34.032=1.702 \\ \text{Thus, the price of the eleventh printer =34.032-1.702=}32.33 \end{gathered}`

Cost of the twelfth printer

The twelfth printer costs 5% less than the eleventh printer, we thus have

`\begin{gathered} D\text{iscount price on the twelfth printer = }\frac{\text{5}}{100}*32.33=1.617 \\ \text{Thus, the price of the twelfth printer =32.33-1.617=}30.713 \end{gathered}`

Thus, the total cost of 12 printers is evaluated as

Thus, the sum of twelve printers is $496.4

The second option is the correct answer.