An agricultural research facility divides a field with a total area of A acres into n indi… — ACT

An agricultural research facility divides a field with a total area of $A$ acres into $n$ individual test plots of equal size after reserving an area of 12 acres for administrative buildings. Which of the following equations correctly expresses the area, $p$ , in acres, of each individual test plot in terms of $A$ and $n$ ?

$p = \frac{A - 12}{n}$ Answer
B
$p = \frac{A}{n} - 12$
C
$p = \frac{A + 12}{n}$
D
$p = n(A - 12)$
E
$p = \frac{n}{A - 12}$

Answer

The equation representing the area of each test plot is

p = \frac{A - 12}{n}

Reserving 12 acres leaves

A - 12

acres available for testing. Dividing this remaining quantity equally into

n

test plots results in an area per plot of

p = \frac{A - 12}{n}

Step-by-Step Solution

Determine the remaining area allocated for test plots.

Available area =

A - 12

acres.

The 12 acres used for administrative buildings must be subtracted from the total field area

A

Divide the remaining area by the number of equal test plots

n

p = \frac{A - 12}{n}

Dividing the remaining acreage equally among

n

plots gives the area

p

of a single plot.

Key Concept

Translating contextual verbal scenarios into basic algebraic expressions using grouping and division.

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