Help with algebra, please!

Question

A rectangle with an area of 240^2 has a length 10 inches shorter than 5 times it's width. Which expression could be used to solve for the length of the rectangle?

Answer 1

We know that the area of a rectangle is the length times the width:

 

A = l x w

 

They tell us that the area is 240 in² (I'm not sure if that's supposed to be 240², or 240 in² but I'm assuming 240 in²), so

 

A = 240

 

Now the length is 10 inches shorter than 5 times the width. If you were 10 inches shorter than me, you would take however tall I am and subtract 10. You're going to use that same concept here to get:

 

l = 5w - 10

 

And nothing special about the width.

 

So putting it all together, we get that:

 

  A  =       l      x   w

   ↓           ↓          ↓

240 = (5w-10) x (w) 

 

Now you just need to distribute the w and then solve for w (it will be a factorable quadratic equation)

 

I know your question doesn't require you to solve, but it's useful to practice wherever you can.