# word problem help

• Mar 24th 2010, 02:36 AM
mjoshua
word problem help
Here's my word problem that I've been meddling with:

The area of a rectangular piece of poster board is 220 square inches. A rectangular photograph that is twice as tall as it is wide is glued to the poster board so that the poster board extends 3 inches beyond the photograph on the top and bottom and 2 inches beyond the photograph on the left and right sides. How many inches wide is the photograph?

There is a rough sketch that is in my book but I've been having trouble saving it on my end to attach it here. Not sure if it helps, but the answer given is supposed to be 7.
• Mar 24th 2010, 03:17 AM
Stroodle
You need to solve

\$\displaystyle (x+4)(2x+6)=220\$

Where \$\displaystyle x\$ is the width of the photo.
• Mar 24th 2010, 03:20 AM
sa-ri-ga-ma
Proceed as given in he above post.
• Mar 24th 2010, 03:28 AM
mjoshua
That certainly works! Thanks! But how did you arrive at the formula for it above?
• Mar 24th 2010, 03:39 AM
Stroodle
No probs :)

If you draw a picture you can see that the width of the poster is \$\displaystyle x+2+2\$, and the height of the poster is \$\displaystyle 2x+3+3\$ (where \$\displaystyle x\$ is the width of the photo).

They've given you the area of the poster as 220. So the width of the poster multiplied by the height of the poster equals 220.
i.e. \$\displaystyle (x+2+2)(2x+3+3)=220\$
• Mar 24th 2010, 11:11 AM
mjoshua
Thanks Stroodle, I think I got it--so you let x be the width and the length is also part of the length.
• Mar 24th 2010, 12:21 PM
Stroodle
Yep, that's correct. You can do this because it says that the photo's height is twice its width.
• Mar 24th 2010, 12:44 PM
mjoshua
thanks :)