Lower Elementary
Question: Billy starts reading a 68 page book on Monday. If he reads 5 pages a day during the week and 7 pages a day during the weekend. On which day of the week will Billy finish his book?
Answer: Saturday
Note: Monday through Friday Billy reads a total of 25 pages (5 pages a day for 5 days, so 5 five times is 25). On the weekend he reads 14 pages (7 pages a day for 2 days, so 7 two times is 14). Knowing that Billy has a total of 68 pages, lets see how close we can get without going over.
Week 1:
Mon. thru Fri.: 25 pages
Sat. & Sun.: 14 pages
Total: 39 pages
Week 2:
Mon. thru Fri.: 25 pages
Total: 64 pages
Without the weekend of week 2, Billy has already read 64, 4 away from finishing the book and now only needs one more day to finish. On Saturday he would have read 7 pages, but since there are only 4 pages to read he finishes reading his book on Saturday.
Upper Elementary
Question: A movie theater has 20 rows of 30 seats each. One night during a movie there were, on average 4 empty seats per row. How many people were watching the movie?
Answer: 520 people
Note: We first need to find the total seats the theater holds. This can be found by multiplying 20 rows by 30 seats.
20 x 30 = 600 seats
Next we need to find how many seats are empty. We know that for every row there are 4 empty seats. This can be done by multiplying 20 rows by 4 seats.
20 x 4 = 80 seats
Now subtract the empty seats from the total seats and this will give us how many seats are occupied.
600 – 80 = 520 seats
Middle School:
Question: In order for a space shuttle to remain in Earth’s orbit it has to travel 17,500 miles per hour. If the shuttle is 4200 miles away from Earth’s core, how many times does this shuttle circle the earth in a day?
Answer: About 16 times
Note: We start by finding the circumference of the path the shuttle orbits around the earth. In the problem it is stated that the shuttle’s orbit has a radius of 4200 miles starting from the center of the earth. Using the circumference formula, we can find how many miles the shuttle has to fly in order to circle the earth once.
C = 2πr ≈ 2(3.14)(4200 miles) ≈ 26376 miles
Dividing the circumference by the speed of the shuttle will give us how long it will take for the space shuttle to circle the earth once.
26376 miles ÷ 17500 miles/hours ≈ 1.5 hours
Finally, since it takes the space shuttle roughly 1.5 hours to circle the earth, we just divide this number into the number of hours in a day, 24.
24 ÷ 1.5 ≈ 16 times
Algebra and Up:
Question: A four digit passcode with non repeating numbers is used to open a safe. The first two digits are odd and the last two digits can be any number from 0 to 9. How many different combinations can this safe have?
Answer: 1120 combinations
Note: Of the digits 0 through 9, there are five odd numbers to choose from for the first digit. After choosing an odd number we cannot choose the same number again because the problems says the numbers are “non-repeating.” Because of this, for the second digit, we only have four odd numbers to choose from.
The last two digits can be any number 0 through 9, but again, because they passcode has no repeating numbers we can only choose eight different numbers since two have already been taken. After the first three numbers have been chosen we only have seven numbers left to choose for the last digit. Multiplying the number of choices per digit will give us how many different combinations this four digit passcode has.
5 • 4 • 8 • 7 = 1120 combinations