Question

select the correct answer.
the number of plants needed to fill a row in a farmers field varies inversely as the distance between the plants. if 72 plants are needed when the plants are 24 centimeters apart, how many plants will be needed if the plants are 32 centimeters apart?
80
54
64
96

Explanation:

Step1: Define inverse variation formula

Let $n$ = number of plants, $d$ = distance. Inverse variation: $n = \frac{k}{d}$, where $k$ is constant.

Step2: Solve for constant $k$

Substitute $n=72$, $d=24$:
$72 = \frac{k}{24}$
$k = 72 \times 24 = 1728$

Step3: Find $n$ for $d=32$

Substitute $k=1728$, $d=32$:
$n = \frac{1728}{32} = 54$

Answer:

B. 54