Two of the team members head toward a stand with a big sign proclaiming “Prize-winning peaches! Picked fresh today!” To their dismay, when they get there, the farmer is just taking down the sign. When they ask why, the response is “Sold out!” The teammates object, “But we’re only two hours into the fair.” The farmer responds, “Well, I sold four fifths of my peaches, plus two fifths of a peach, in the first half hour of the fair. And as it happens I sold four fifths of what remained plus two fifths of a peach in the second half hour of the fair. And remarkably, in the third half hour of the fair I sold four-fifths of what I had at the beginning of that half hour, plus two-fifths of a peach. And just in the past half hour I’ve sold four fifths of what was left after the first 90 minutes, plus two-fifths of a peach. And that resulted in all of my peaches being gone.” “That must have been messy, cutting up all of those peaches,” say the teammates. “Nope,” says the farmer, “I didn’t have to cut a single peach all morning.”
How many peaches did the farmer bring to the fair?
A Day Late and A Fence Short
Wandering away from the disappointing peach stand, the team members encounter a puzzled-looking fair official. “What seems to be the problem?” they ask.”Well, you see, kids, we were supposed to have thirteen identical 10-foot fence panels to make six identical pens for the six finalists in the state hog-raising competition, as shown in this diagram. But somehow only twelve panels got on the truck. Now we’re not going to have anywhere to put the sixth pig.” The team members respond, “Don’t worry, we can show you how to rearrange things to make six identical pens with only twelve fence sections.” The official asks, “Are you sure? The owners say that each pig must have at least 40 square feet of space in its pen.” The team members assure the official that their plan will work.
Draw the arrangement of fences that the team members suggest.