Lower Elementary:
Question: Neil began the week with $2 worth of quarters. At the end of the week, he had 23 quarters. How many quarters did Neil receive throughout the week?
Answer: 15 quarters
Solution: To find how many quarters Neil received throughout the week, we take the total number of coins he ended the week with and subtract from the number of quarters he started with. He started the week with $2 worth of quarters, which is 8 quarters. 23 – 8 = 15. He received 15 quarters throughout the week.
Upper Elementary:
Question: Laurie has blue, red, and black pens in her pen case. Half of her pens are blue, 1/5 are red, and the remaining 9 pens are black. How many pens does Laurie have?
Answer: 30 pens
Solution: We need to find the fractional part that the black pens represent since we know how many total black pens there are. To find a part, we can take the whole and subtract the sum of the other parts. 1 – 1/2 – 1/5 = 1/2 – 1/5 = 5/10 – 2/10 = 3/10. The black pens represent 3/10 of the total pens. If 3/10 represents 9 pens, then 1/10 represents 3 pens. That means that the total number of pens in the pen case is 30 pens.
Middle School:
Question: In the expression 35 + 0.5(3x – 4)2, Grace substituted 2 for x and got 37 doing it by hand but got 43,681 by putting it in a simple calculator. Which is the correct answer and why?
Answer: 37, Grace followed the order of operations
Solution: In order to simplify this problem, we need to follow the order of operations. First is parentheses, so we do what is in the parentheses first. Since we are substituting 2 for x, we have 3 • 2 – 4 = 6 – 4 = 2 for the inside of the parentheses. Now our expression is 35 + 0.5(2)2. Next is exponents. Now our expression is 35 + 0.5(4). Next is multiplication and/or division. 35 + 2. Finally, it is addition and/or subtraction. 37. So Grace was correct doing it by hand because she followed the order of operations.
Algebra and Up:
Question: Two boats start at the same dock. One boat travels 30 mph going north. The other boat travels 40 mph going west. If the both travel in a straight line, how far apart will the boats be after 30 minutes?
Answer: 25 miles
Solution: If they each travel for 30 minutes, or half an hour, then the first boat travels 15 miles north and the other boat travels 20 miles west. The shape that is made is a right triangle, with the lengths of the legs being 15 and 20. To find the length of the third side, we can use the Pythagorean Theorem.
152 + 202 = c2
225 + 400 = c2
625 = c2
25 = c
The boats are 25 miles apart from each other.
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