Lower Elementary
Question: This week Fred saved 1/6 of his allowance in order to buy a video game. If the amount of money he saved was $5, how much money did he get for allowance this week?
Answer: $30
Note: If Fred saved 1/6 of his allowance, that would be like taking the total amount of his allowance, splitting it into six equal parts and keeping one of the parts. We know one of the parts is $5. That means each of the six parts of his allowance is worth $5. This means the entire allowance was ($5 x 6) $30.
Upper Elementary
Question: Frank is building a bookcase. In order to complete the job he cut a piece of wood that is 18 feet long into three pieces. The shortest piece is half as long as the middle-sized piece and the longest is three times as long as the shortest piece. How long is each piece of wood?
Answer: shortest piece = 3 feet, middle-sized piece = 6 feet, longest = 9 feet
Note: For this problem each piece will have a whole number measurement. Use guess and check method. A good way to start is to begin with a measurement for the third piece, then using that value find the measurement of the first and second piece of wood. Find the sum. Depending on the result adjust the initial guess.
Middle School
Question: The volume of a cube is 8 in3. A new cube is formed by quadrupling the length of each side of the original cube. How many times larger is the volume of the new cube than the volume of the original cube?
Answer: 64 times larger
Note: The length, width, and height of a cube are equal. Given that the volume of a cube = length x width x height, then if the original cube has a volume of 8 then the length, width, and height of the cube must equal 2 inches ( 2 x 2 x 2 = 8). To make the new cube, the length, width, and height of the original cube is quadrupled (multiplied by 4) respectively. That means for the new cube each dimension is equal to (2 x 4) 8 inches.
To find the volume of the new cube multiple: 8 in x 8 in x 8 in = 512 in3.
Then divide the volume of the new cube by the volume of the original cube to find out how many times larger the new volume is than the original volume.
512 / 8 = 64.
Algebra and Up
Question: The product of two positive consecutive even integers is 224. What are the two integers?
Answer: 14 and 16
Note: One method for solving this problem is the guess and check method.
Another method would be to set up an equation and solve.
x = the first positive even integer
x + 2 = the next even integer
Then the product is: x(x + 2)
The equation is x(x + 2) = 224. Now solve.
x(x + 2) = 224
x2 + 2x = 224 (now subtract 224 from both sides)
x2 + 2x – 224 = 0 (now factor the left side of the equation)
(x + 16)(x – 14) = 0
Solving, we find x = -16 or 14. Since x has to be positive then x = 14. That means the next even integer is 16 (14 + 2).
