In high school I recall having a beautiful but difficult math teacher. She was easy on the eyes but hard on the pupils.
Question: Joshua’s mom puts 8 coins in his piggy bank and said “I put in 47 cents.” Three of the coins she put in were nickels. What were the coins that Joshua’s mom put into his piggy bank?
Question: You are figuring out what time to set your clock in the morning to wake up. It takes you 15 minutes to eat breakfast, 22 minutes to shower, 14 minutes to get dressed, and 35 minutes to walk to school. If school starts at 8:05 AM, what is the latest you can set your alarm so that you are still on time?
Question: There are 4-sided dice that are labeled with numbers 1 through 4. If you roll three 4-sided dice at the same time, what is the probability that the sum of the three dice is 3, 4, 11, or 12?
Algebra and Up
Question: The sum of 6 consecutive odd integers is 192. What are the 6 numbers?
Answer: 3 Dimes, 3 Nickels, and 2 Pennies
Solution: The value of the three nickels is 15 cents (5 + 5 + 5 = 15 cents). If we subtract the value of the nickels from the total, we have 32 cents left. If we subtract the number of nickels from the total coins, we have five coins left. Two of the coins must be pennies because any other coin would make the total value end with a 5 or 0. Now we have three coins that total 30 cents. The only three coins that total 30 are 3 dimes. So the coins in the bank are 3 dimes, 3 nickels, and 2 pennies.
Answer: 6:39 AM
Solution: The total time it takes to do the morning routine is 1 hour and 26 minutes (15 + 22 + 14 + 35 = 86 minutes = 1 hour 26 minutes). To know what time to set the alarm, we go back 1 hour to 7:05 AM and then back 26 minutes to 6:39 AM.
Answer: 1/8 or 12.5%
Solution: We first must find the total number of possible outcomes. Each die has 4 possible outcomes, so the total number of outcomes is 64 (4 × 4 × 4 = 64). Now we need to find the total number of ways of rolling a 3, 4, 11, or 12. Let’s list all the possible outcomes for each:
3: (1,1,1). One way
4: (1,1,2), (1,2,1), (2,1,1). Three ways
11: (4,4,3), (4,3,4), (3,4,4). Three ways
12: (4,4,4). One way
So the total possible ways for us to roll a sum of 3, 4, 11, or 12 is 8. There are a total of 64 outcomes. So the probability is 8/64 which reduces to 1/8, which is 12.5%.
Algebra and up:
Answer: 27, 29, 31, 33, 35, and 37
Solution: Let’s call the smallest number n. Since the numbers are consecutive odd integers, if the first number is n, then the next odd number is two more, n + 2, and the next one is n + 4, and so on. Using this we can write an equation for the 6 numbers:
n + (n+2) + (n+4) + (n+6) + (n+8) + (n+10) = 192 6n + 30 = 192 6n = 162 n = 27
The first number is 27 and the rest of the numbers are the next 5 consecutive odd integers. So the 6 numbers are 27, 29, 31, 33, 35, and 37.