Lower Elementary
Question: In two years Sharon will be twice as old as her sister Jennifer. The sum of their ages today is 14. How old is Jennifer?
Answer: 4 years old
Note: Use guess and check method.
Upper Elementary
Question: Use the list of numbers below.
9 14 5 13 10 3 7 8 6 2
Cross out two numbers with a difference of 6 and a product of 91. Then cross out two numbers with a a sum of 13 and a difference of 3. Next, cross out two numbers that have a quotient of 5 and a difference of 8. Finally cross out tow numbers with a difference of 6 and a quotient of 3. What is the sum of the numbers that are left?
Answer: 20 (numbers that are left are 14 and 6)
Note:
1. There are three pairs of numbers with a difference of 6. 9 and 3, 13 and 7, and 8 and 2. However only 13 and 7 have a product of 91. Cross out 13 and 7.
2. There are two pairs of numbers with a sum of 13. 8 and 5 and 10 and 3. However, only 8 and 5 have a difference of 3. Cross out 8 and 5.
3. There is only one pair of numbers left that has a quotient of 5 and difference of 8, 10 and 2. Cross out 10 and 2.
4. There is finally only one pair of numbers that have a difference of 6 and a quotient of 3, 9 and 3. Cross out 9 and 3.
The numbers that are left are 14 and 6.
Middle School
Question: The area of a square is 40 square inches. A new square is made by quadrupling each of the side lengths of the original square. What is the area of the new square?
Answer: 640 square inches.
Note: The area of a square is equal to side times side. A = s x s = s2. If each of the sides is quadrupled then the new side length is 4 times s or 4s. That means the area of the new square is 4s x 4s. That means the new square has an area of 16(s x s) or 16s2. If the area of the original square is 40 then the area of the new square is 16 x 40 = 640.
Algebra and Up
Question: A sculpture garden has two different sized sculptures in the shape of rectangular prisms. The larger rectangular prism weighs 4 tons. Each dimension of the smaller prism is one quarter of those of the larger prism. Find the weight of the smaller prism (in pounds).
Answer: 125 pounds
Note: The weight of the larger prism in pounds is 8000. (1 ton = 2000 pounds.) To find the weight of the smaller prism find the fraction the smaller prism is of the larger prism. The volume of the larger prism is V = l x w x h. Since each dimension of the smaller prism is 1/4 of each dimension of the larger prism, the volume of the smaller prism is 1/4l x 1/4w x 1/4h = 1/64V. That means the smaller prism is 1/64 of the larger prism. The weight of the prism will be 1/64 of the larger prism. 1/64 x 8000 pounds = 125 pounds.