Problem of the Week 08-22-16

Lower Elementary:
Question: Babs has a handful of 24 cheese crackers. If she eats half of them, then eats half of what’s left, how many cheese crackers will Babs have left?
Answer:  6 cheese cracker
Solution:  Half of 24 is 12, so Babs will have 12 crackers left after she eats half of them. Half of 12 is 6, so she will have 6 crackers left after she eats half of half the cheese crackers.

Upper Elementary:
Question: Each candle will burn for 30 minutes. How many candles will you need for a power outage that lasts 3 hours and 45 minutes?
Answer:  71/2 candles
Solution:  One candle lasts half an hour, so 2 candles last an hour. For the first 3 hours, you will need 3 × 2 = 6 candles. That leaves another 45 minutes, which is exactly between half an hour and a full hour, so you’re going to need another candle and a half because 11/2 is exactly between 1 and 2 candles. That makes a total of 6 + 11/2 = 71/2 candles.

Middle School:
Question: What’s the probability of tossing the same face of a coin in a fair coin toss three times in a row?
Answer:  1 out of 4
Solution:  Let’s say we want to toss just heads. Each toss has a one out of 2 chance of landing on heads. So, the chance of tossing 2 heads in a row is 1/2 × 1/2 = 1/4. For the last toss, the probability of tossing heads is one out of 2 again, so we multiply 1/4 × 1/2 = 1/8. So, the probability of tossing 3 heads in a row is 1 out of 8. You have an equal chance of tossing all tails, too, so the probability of tossing all the same face in a fair coin toss is 1/8 + 1/8 = 1/4, or 1 out of 4.

Algebra and Up:
Question: A bunch of bananas and a cantaloupe together weigh 6 pounds. A papaya and a cantaloupe together weigh 5 pounds. A papaya and a bunch of bananas together weigh 4 pounds. Find the weight of each fruit.
Answer:  The bananas weigh 2.5 pounds, the cantaloupe 3.5 pounds, and the papaya weighs 1.5 pounds.
Solution:  The first two pairs, bananas + cantaloupe and papaya + cantaloupe, have the cantaloupe in common, but bananas + cantaloupe is 1 pound heavier than papaya + cantaloupe, so the bananas must be 1 pound heavier than the papaya: B = P + 1. We also know that the bananas and papaya together weigh 4 pounds: B + P = 4. If we substitute P + 1 in for B in the second equation, we find that 2P + 1 = 4, so 2P = 3, so P = 1.5 pounds. From there, we can find that the bananas weigh 2.5 pounds and the cantaloupe weighs 3.5 pounds.