Question

Select the correct answer. Brad is planting flowers in a grid-like pattern in his garden. He is trying to determine the possible numbers of rows and columns in which he can plant his flowers. He determines that two possibilities are 8 rows and 25 columns or 10 rows and 20 columns. What is the constant of proportionality in this inverse variation?

Answer 1

Answer:

$C.\ 200$

Step-by-step explanation:

Given

Let R represents rows and C represents Columns

When R = 8, C = 25

When R = 10, C = 20

Required

Given that there exist an inverse variation, determine the constant of proportionality;

We start by representing the variation;

$R\ \alpha \ \frac{1}{C}$

Convert proportion to an equation

$R\ = \ \frac{k}{C}$

Where k is the constant of proportion;

$R * C\ = \ \frac{k}{C} * C$

Multiply both sides by C

$R * C\ = k$

Reorder

$k = R * C$

When R = 8, C = 25;

The equation  $k = R * C$ becomes

$k = 8 * 25$

$k = 200$

When R = 10, C = 20;

The equation  $k = R * C$ becomes

$k = 10 * 20$

$k = 200$

Hence, the concept of proportionality is 200