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

`C.\ 200`

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 \ (1)/(C)`

Convert proportion to an equation

`R\ = \ (k)/(C)`

Where k is the constant of proportion;

`R * C\ = \ (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