Lower Elementary:
Question: Jack needs to take a train that leaves at 3:30 PM. He is going to stop at a sandwich shop at the train station for 30 minutes to get some food. He needs to wait in line for 5 minutes to buy his ticket. He needs 10 minutes to find the platform for his train. If it takes him 35 minutes to walk to the train station, what time should Jack leave in order to make it to his train on time?
Answer: 2:10 PM
Solution: First, let’s find the total time Jack needs for all of his actions. 30 minutes for eating, 5 minutes for tickets, 10 minutes for finding the platform, 35 minutes for walking. 30 + 5 + 10 + 35 = 80 minutes. Since 60 minutes becomes 1 hour, 80 minutes = 1 hour and 20 minutes. Count backwards from 3:30 PM to find the time Jack needs to leave by. First, subtract the hour, 2:30 PM. Then subtract 20 minutes and we have 2:10 PM. Jack needs to leave at 2:10 PM to make it to the train on time.
Upper Elementary:
Question: I am a 4 digit number. Each of my digits are prime numbers and each digit is different. I am an even number. My hundreds digit is the largest digit. I am larger than 4,000. What number am I?
Answer: 5,732
Solution: Since each digit is a prime number, our only choices for digits are 2, 3, 5, and 7. The number is even, so it has to end with a 2 since 2 is the only even number in the list. 7 is the largest number so 7 goes in the hundreds place. So our 2 possible numbers are 3,752 or 5,732. Since the number is larger than 4,000 the mystery number is 5,732.
Middle School:
Question: Sara gets paid $15.00 an hour. She worked 80 hours during the pay period. If 28% of what she earned is deducted for taxes, how much does Sara get to take home?
Answer: $864
Solution: First, find out how much money Sara earned in total during the pay period. 15 × 80 = 1,200. She earned $1,200. If 28% of her paycheck is taken away, that means she keeps 72% of her paycheck (100% – 28% = 72%). To find out how much money Sara gets to keep, find 72% of 1,200. Percent means for each hundred. There are 12 hundreds in 1,200. This problem becomes what is 72, 12 times. 72 × 12 = 864. Sara keeps $864 of her paycheck.
Algebra and Up:
Question: You have two similar triangles. The side length of the largest side of the bigger triangle is 10 cm. The side length of the largest side of the smaller triangle is 10 mm. If the area of the bigger triangle is 30 square cm, what is the area of the smaller triangle?
Answer: 0.3 cm2
Solution: First, we convert the units for one of the triangles so they have the same unit, because we can only compare things with the same name. 10 mm = 1 cm. The length of the largest side of the bigger triangle is 10cm and the length of the largest side of the smaller triangle is 1 cm. Since they are similar, the ratio of the sides from the bigger triangle to the smaller triangle is 10:1. One way to solve this is to use the fact that the area of two similar triangles is proportional to the ratio between the triangles squared. If we set this up we get:
A1/A2 = m2/n2 where A1 is the area of the larger triangle, A2 is the area of the smaller triangle, and m/n is the ratio between the triangles. Plugging in what we have we get:
30/A2 = 102/12
30/A2 = 100/1
30 = 100A2
A2 = 30/100 = 3/10 = 0.3 cm2.
The area of the smaller triangle is 0.3 cm2.
