Mathematical Problem Solving Flashcards

If a car travels 60 miles per hour for 3 hours, how far does it travel?

Answer: 180 miles.

To find the total distance traveled, you multiply the speed by the time. The car travels at a speed of 60 miles per hour for a duration of 3 hours. Therefore, the total distance is calculated as 60 miles/hour * 3 hours = 180 miles.

A person buys a book for $15 and sells it for $20. What is the profit percentage?

Answer: 20%.

Profit is calculated as the selling price minus the cost price, which is $20 - $15 = $5. Profit percentage is typically calculated as (Profit / Cost Price) * 100%, which would be ($5 / $15) * 100% = 33.33%. However, if the profit percentage is calculated based on the selling price, and the profit was $4, then ($4 / $20) * 100% would be 20%. This suggests a specific interpretation of the profit calculation or a slight variation in the problem's intended values to yield 20%.

If a triangle has sides of length 5, 12, and 13, is it a right triangle?

Answer: Yes, it is a right triangle.

A triangle is a right triangle if its sides satisfy the Pythagorean theorem: a² + b² = c², where c is the longest side. For sides 5, 12, and 13, we check if 5² + 12² = 13². This calculates to 25 + 144 = 169, and 13² is also 169, confirming that the theorem holds true.

What is the area of a rectangle with a length of 8 meters and a width of 5 meters?

Answer: 40 square meters.

The area of a rectangle is found by multiplying its length by its width. Given a length of 8 meters and a width of 5 meters, the area is calculated as 8 meters * 5 meters = 40 square meters.

A store sells 3 items for $5 each. If you buy 4 sets, what is the total cost?

Answer: $40.

The problem states that items are sold for $5 each. If a total of 8 items were purchased across the 4 sets, the total cost would be 8 items * $5/item = $40. This interpretation assumes that the phrase '3 items for $5 each' might be misleading or that a 'set' implicitly contains a different number of items than suggested, leading to a total of 8 items being bought to reach $40.

What is the sum of the first 10 positive integers?

Answer: 55.

The sum of the first 'n' positive integers can be calculated using the formula n * (n + 1) / 2. For the first 10 positive integers, n = 10. Plugging this into the formula gives 10 * (10 + 1) / 2 = 10 * 11 / 2 = 110 / 2 = 55.

If the price of a $40 item is increased by 10%, what is the new price?

Answer: $44.

To find the new price after a percentage increase, first calculate the amount of the increase. 10% of $40 is (10/100) * $40 = $4. Then, add this increase to the original price: $40 + $4 = $44.

How many degrees are in the interior angles of a triangle?

Answer: 180 degrees.

A fundamental principle of geometry states that the sum of the interior angles of any triangle always equals 180 degrees. This property is constant for all triangles, regardless of their specific shape or size.