Lower Elementary:
Question: Fiona starts trick-or-treating at 6:30 PM. She spends 30 minutes on Walker Road, 20 minutes on Mulberry Street, and 25 minutes on Glen Court. She then takes 10 minutes to walk back home. What time does Fiona come back home after trick-or-treating?
Answer: 7:55 PM
Solution: Fiona starts at 6:30 PM. She spends 30 minutes on the first street, so now the time is 7:00 PM. She spends 20 minutes on the second street, so now the time is 7:20 PM. She spend 25 minutes on the third street, so now the time is 7:45 PM. She takes 10 minutes to go home, so now the time is 7:55 PM.
Alternatively, if we add 30 + 20 + 10, that is 60 minutes, which is the same as 1 hour. That makes the time 7:30 PM. With only 25 minutes left to add, 25 minutes past 7:30 PM is 7:55 PM.
Upper Elementary:
Question: Howard’s mother is going to bake pumpkin seeds. She buys 6 pumpkins. 2 pumpkins contain 50 pumpkin seeds each and the remaining pumpkins contain 75 pumpkin seeds each. When cleaning the seeds, 10 fell down the drain. After the seeds are baked, Howard and his mother ate 30 pieces. How many pumpkin seeds are left?
Answer: 360 pumpkin seeds
Solution: First, let’s find the total number of seeds that they started with. 2 pumpkins contain 50 seeds, so together those pumpkins have 100 seeds (2 × 50 = 100). The remaining 4 pumpkins have 75 seeds, so together those pumpkins have 300 seeds (4 × 75 = 300). Altogether, they start with 400 seeds. 10 fall down the drain and then they ate 30, so that means that 40 seeds are taken away from the total. 400 – 40 = 360. There are 360 pumpkin seeds left.
Middle School:
Question: Casey’s Halloween party is having a costume contest. There is a first place, second place, and third place prize. Out of the 15 guests, 5 dressed as vampires. How many different possible arrangements of winners are there if only one vampire wins a prize and they place second?
Answer: 450
Solution: There are a total of 15 guests. 5 of them are vampires and the remaining 10 are anything else. Since only 1 vampire wins and they win second place, there are 10 people that could win first place. Then one of the 5 vampires wins second place. For third place, it is not a vampire, and there is already a winner for first place, so there are 9 people to choose from. Multiply 10 × 5 × 9 together to get the possible arrangements of winners if only one vampire wins a prize and they place second. 10 × 5 × 9 = 450.
Algebra and Up:
Question: In a bowl are 2 bags of candy. One bag contains 20 pieces of candy: 10 red pieces, 5 green pieces, and 5 yellow pieces. The other bag contains 25 pieces of candy: 10 red pieces, 10 green pieces, and 5 yellow pieces. If you pick a bag at random and then pick a piece of candy at random, what is the probability of drawing a red piece of candy?
Answer: 9/20
Solution: One way to solve this problem is to first find the probability of picking each of the bags. Since there are 2 bags to pick from, there is a 1/2 probability of drawing the 20 piece bag and a 1/2 probability of drawing the 25 piece bag. Now, let’s calculate the probability of picking a red candy from each bag separately.
20 piece bag: there are 20 total pieces and 10 pieces are red. The probability is 10/20 = 1/2.
25 piece bag: there are 25 total pieces and 10 pieces are red. The probability is 10/25 = 2/5.
Now, we need to multiply the probability of drawing each bag to the probability of drawing a red piece from a bag.
20 piece bag: 1/2 × 1/2 = 1/4
25 piece bag: 1/2 × 2/5 = 1/5
Now add the probabilities together to get the probability of drawing a red piece of candy.
1/4 + 1/5 = 5/20 + 4/20 = 9/20.
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