Question

The width, y, of a rectangle with a fixed area varies inversely with its length, x. The width is 3 inches when the length is 14 inches. Find the width when the length is 30 inches.

Answer 1

Answer:

$y = 1.4$

Step-by-step explanation:

Given

$y = width$

$x = length$

$y = 3;\ when\ x = 14$

Required

Find y when x = 30

Being an inverse variation, we have:

$y\ \alpha\ \frac{1}{x}$

Convert the variation to an equation

$y = \frac{k}{x}$

First, we solve for k

Make k the subject to solve for k

$k = xy$

$y = 3;\ when\ x = 14$

So, the value of k is:

$k = 14 * 3$

$k = 42$

To solve for y when x = 30

Substitute 30 for x and 42 for k in $k = xy$

$42 = 30 * y$

Make y the subject

$y = \frac{42}{30}$

$y = 1.4$