Question

The length of a rectangle should be 8 meters longer than 7 times the width. If the length must be
between 43 and 106 meters long, what are the restrictions for the width, x?

Answer 1

Answer:

The restrictions for x would be 14 > x > 5.

Step-by-step explanation:

Let the length of the rectangle be y and the width be x.

That being said, the equation would be as follows:

$y = 7x + 8$

$y - 8 = 7x$

$x = \frac{y-8}{7}$

Therefore, substituting the two values of y into the equations, we would get:

$x = \frac{43-8}{7}$

$x = \frac{35}{7}$

$x = 5$

And:

$x = \frac{106-8}{7}$

$x = \frac{98}{7}$

$x = 14$

Therefore, x would be between 5 and 14, and the restrictions for x would be 14 > x > 5.

Hope this helped!