Lower Elementary:
Question: Nina brought a bag of cheese puffs to a birthday party. The bag had 96 cheese puffs. The guests ate half of the cheese puffs before the cake was served. Half of what was remaining was eaten after the cake was served. How many cheese puffs are left?
Answer: 24 cheese puffs
Solution: The bag started with 96 cheese puffs. Before the cake was served, half were eaten. Half of 96 = half of 90 + half of 6 = 45 + 3 = 48. There were 48 cheese puffs left when the cake was served. Half of what was remaining was eaten after the cake was served. Half of 48 = half of 40 + half of 8 = 20 + 4 = 24. There are 24 cheese puffs left.
Upper Elementary:
Question: What are the next 3 numbers in the pattern?
2, 4, 6, 10, 16, 26, 42…
Answer: 68, 110, 178
Solution: Notice that 6 is formed from 2 + 4 and 10 is formed from 4 + 6. The next number in the pattern is the sum of the two previous numbers. 2 + 4 = 6, 4 + 6 = 10, 6 + 10 = 16, 10 + 16 = 26, 16 + 26 = 42. So, to get the next number in the pattern, we have to add 26 + 42 = 68. The next number is 42 + 68 = 110. The next number is 68 + 110 = 178. So, the next three numbers in the pattern are 68, 110, and 178.
Middle School:
Question: A water tower is 60% filled. 200 gallons of water leaks out and now it is 40% filled. How much water can the water tower hold?
Answer: 1,000 gallons
Solution: The tower started at being 60% filled. When the 200 gallons leaked out, it is now 40% filled. That means that 20% of the water leaked out. Since 200 gallons leaked out, this means that 200 represents 20% of the water that the tower can hold. Percent means for each hundred, so we want to get to 100% to get the total amount of water that the tower can hold. To go from 20% to 100%, we multiply by 5. 200 × 5 = 1,000. The water tower can hold 1,000 gallons of water.
Algebra and Up:
Question: A deck of 100 cards are numbered from 1 to 100. What is the probability of drawing a card that has 3 factors or fewer?
Answer: 30/100 = 3/10 = 30%
Solution: Prime numbers have only 2 factors, so all prime numbers from 1 to 100 are the cards that we want to take into account. To have 3 factors, it must be a prime number that is squared, meaning 2 squared = 4, 3 squared = 9, 5 squared = 25, and 7 squared = 49 are also included in the cards we want to take into account. Also, since 1 only has 1 factor, it is also included. So, all of the numbers that have 3 or less factors are: 1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. There are a total of 30 numbers. So, the probability of drawing a number with 3 factors or fewer is 30/100 = 3/10 = 30%.
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