Lower Elementary
Question: What is the number that is one half of one half of one half of 25?
Answer: 3 1/8
Upper Elementary
Question: Two hours from now it will be half as long until midnight as it will be one hour from now. What time is it now?
Answer: 9 pm
Note: Most students will use a guess and check method for solving this problem.
Middle School
Question: Four years ago, Mark was twice as old as Brian. Four years from now, Brian will be 3/4 of Mark’s age. How old is Brian now?
Answer: 8 years old
Note: There are several ways to solve this problem. The simplest is guess and check.
It is also possible to solve this problem algebraically. Let x = Mark’s age now; y = Brian’s age now. That means Mark’s age 4 years ago is x – 4 and Brian’s age 4 years ago is y – 4. If Mark was twice as old as Brian 4 years ago that means x – 4 = 2 • (y – 4). 4 years from now x + 4 = Mark’s age and y + 4 = Brian’s age. Brian will be 3/4 of Mark’s age. y + 4 = 3/4 • (x + 4). Now you have two equations and two unknowns. Solving the system gives x = 12 and y = 8.
Algebra and Up
Question: Alex and Sarah start in the same place and walk 6 yards in opposite directions. Then, they turn right and walk another 8 yards. What is the distance between them?
Answer: 20 yards.
Note: Drawing a picture helps to see that both Alex and Sarah are walking along the legs of right triangles, measuring 6 yards and 8 yards. The distance between them is 2 times the length of the hypotenuse of the right triangle (10 yards) which is 20 yards. You can solve either by using Pythagorean Theorem or noticing the Pythagorean triple 6, 8, 10.
