Lower Elementary
Question: A new candle that is 8 inches long, burns for 4 hours. How long will the candle be after burning for 3 hours?
Answer: 2 inches.
Note: Assume candles burn at a uniform rate. If the candle burns for 2 hours it will be 4 inches long (half it’s length). So that means for another 1 hour it will lose half of 4 inches which is 2 inches. Altogether it has lost 6 inches so it will be 2 inches tall.
Upper Elementary
Question: Eric is having a party at his house. He wants to buy hot dogs and buns. If hot dogs come in packages of 10 and buns come in packages of 8. How many of each package should he buy so that he has the same number of hot dogs and buns?
Answer: 4 packages of hot dogs and 5 packages of buns.
Middle School
Question: A triangle has side lengths that are whole numbers. If two of the side lengths are 8 cm and 9 cm, what is the largest possible value of the length of the third side?
Answer: 16 cm
Note: The length of the third side of a triangle has to be greater than the difference of the other two sides and less than the sum of the other two sides. For a triangle with sides 8 cm and 9 cm, that means greater than 1 and less than 17. Since all the side lengths are whole numbers the largest value of the length of the third side is 16. This problem assumes the triangle is not a degenerate triangle.
Algebra and Up
Question: Four times the complement of an angle is the same as the sum of 36Ëš and the same angle’s supplement. What is the measure of the angle?
Answer: 48Ëš
Note: Complementary angles add up to 90Ëš. Supplementary angles add up to 180Ëš. Let x = the unknown angle. Then the complement of the angle is 90 – x and the supplement is 180 – x.
Four times the complement would be 4(90 – x) and the sum of 36 and the supplement is 180 – x + 36. Since these are the same we set them equal.
4(90 – x) = 180 – x + 36. Then solve for x.
360 – 4x = 216 – x
48 = x
