I’m in Los Angeles this weekend visiting friends. It’s sunny here, and even though it’s actually not that all that warm, the palm trees make it feel that way. I know that many of you, however, are not on vacation, and that actually some of you are taking the December SAT tomorrow. If that’s you, good luck!

There’s no prize this week–just bragging rights. When the book is done, I’ll figure out creative ways to give prizes again.

John is putting his favorite movie posters in frames to hang in his house. It costs John \$75 for a frame that measures 30 inches by 50 inches. It costs him \$125 for a frame of similar construction but with dimensions of 40 inches by 55 inches. If 30% of the price increase is the cost of the additional wood needed for the outside of the frame, what is the cost of one foot of the wood?

Have fun, folks. I’ll post the solution early next week (might actually not be Monday or even Tuesday due to travel). Bonus bragging rights for the most coherent explanation in the comments before then.

(Side note: I know a few of you are waiting on me to answer Tumblr questions. I will probably not get to them until Monday or Tuesday since my computer time is limited.)

UPDATE: Nice work, emolano. Solution below.

This one is deceptive. The price difference between the two frames is \$50. 30% of that is \$15. Since the dimensions increase from 30×50 to 40×55, it’s tempting to say that you’re looking at a 15 inch increase in the amount of wood needed, and that the wood costs \$1/inch. But if you did that…you’d be wrong.

If that frame is going to be rectangular, you have to add wood to all four sides of the frame! That means you’re really adding 30 inches of wood. So the price increase is \$15 for 30 inches of wood, or \$0.50 per inch. Since there are 12 inches in a foot, the wood costs \$6 per foot.