Question

multiple choice 1 point
a rectangular lot with a 97 - ft frontage and a 266 - ft depth sold for $13,500. assuming the cost per square foot remains the same, find the price of a rectangular lot with a 78 - ft frontage and a 211 - ft depth. (round your answer to the nearest dollar.)
$8,767
$8,611
$8,206
$8,328
$9,082

Explanation:

Step1: Calculate area of first lot

The area $A_1$ of a rectangle is length times width. For the first lot, with frontage (width) $w_1 = 97$ ft and depth (length) $l_1=266$ ft, $A_1=w_1\times l_1=97\times266 = 25802$ square - feet.

Step2: Calculate cost per square - foot of first lot

The first lot sold for $C_1 = 13500$ dollars. The cost per square - foot $k$ is $k=\frac{C_1}{A_1}=\frac{13500}{25802}\approx0.5232$ dollars per square - foot.

Step3: Calculate area of second lot

For the second lot, with frontage (width) $w_2 = 78$ ft and depth (length) $l_2 = 211$ ft, $A_2=w_2\times l_2=78\times211 = 16458$ square - feet.

Step4: Calculate price of second lot

The price $C_2$ of the second lot is $C_2=k\times A_2$. Substituting $k\approx0.5232$ and $A_2 = 16458$, we get $C_2\approx0.5232\times16458\approx8611$ dollars.

Answer:

$8611$ dollars, so the answer is B. $8,611$