Lower Elementary:
Question: There are 92 cars in a parking lot. Half of the cars have four doors. Half of the cars with four door are blue. How many blue four-door cars are there?
Answer: 23 cars
Solution: Half of the 92 cars in the parking lot have four doors. Half of 92 = half of 80 + half of 12 = 40 + 6 = 46. There are 46 cars that have four doors. Half of the four door cars are blue. Half of 46 = half of 40 + half of 6 = 20 + 3 = 23. There are 23 blue four-door cars in the parking lot.
Upper Elementary:
Question: For a video game, your game team is has many characters. In this game, half of the team are spell casters, two fifths of the team are warriors, and the remaining 3 team members are dragon tamers. How many total team members are there?
Answer: 30 party members
Solution: One way to solve this problem is to find the fractional part of the team that represents the dragon tamers and then use that to find the total number of team members. To find the part, take the whole and subtract the sum of the other parts. 1 – 1/2 – 2/5. In order to subtract fractions, they need to have the same denomination, or same name. 1/2 = 5/10 and 2/5 = 4/10. 1 – 5/10 –4/10 = 1/10. So, the dragon tamers represent 1/10 of the party. Now we need to find 1/10 of what number is 3. 1/10 of 30 is 3, so there are 30 members in the party.
Middle School:
Question: Nina has a circular mirror that has a frame around it. The frame has a radius of 6 inches and the mirror itself has a diameter of 10 inches. If the mirror is centered in the frame, what area of the frame is not covered by the mirror?
Answer: 11π square inches, or approximately 34.54 square inches
Solution: One way to solve this problem is to subtract the area of the mirror from the area of the frame. The area for a circle is Area = πr2. The radius of the frame is 6. So, the area of the frame is π(6)2 = 36π square inches. The diameter of the mirror is 10 inches, so the radius is 5 inches. The area of the mirror is π(5)2 = 25π square inches. Now let’s subtract the area of the mirror from the area of the frame. 36π – 25π = 11π square inches. The area of the frame that is not covered by the mirror is 11π square inches, or approximately 34.54 square inches.
Algebra and Up:
Question: A bottle rocket is launched from a pad. It’s altitude at any point in its flight can be determined by the function y(t) = –6t2 + 71t + 12, where y is how high off the ground it is in feet and t is the time since it is launched in seconds. How long was the rocket in the air after it was launched from the pad?
Answer: 12 seconds
Solution: When the rocket hits the ground, it is 0 feet off of the ground. So, our equation becomes 0 = –6t2 + 71t + 12. This will tell us the time when it hit the ground, which is the same as how long the rocket was in the air. We need to solve this equation for t. One way to do this is to factor the equation.
0 = –6t2 + 71t + 12
Factor the right side of the equation.
0 = (–6t – 1)(t – 12)
Set each factor equal to 0 and solve for t.
–6t – 1 = 0
–6t = 1
t = –1/6
And now for the other factor.
t – 12 = 0
t = 12
Therefore, the two values for t are –1/6 seconds and 12 seconds. Time cannot be negative in this problem, so the bottle rocket hit the ground 12 seconds after being launched from the pad, meaning it was in the air for 12 seconds.
