Lower Elementary:
Question: Gretchen dropped her car off at the repair shop to get fixed at 10AM. She walked 20 minutes to the mall, browsed the shops for an hour and a half, spent 30 minutes eating lunch, and then walked 20 minutes back to the car shop to pick up her car. What time did Gretchen pick up her car?
Answer: 12:40PM
Solution: Gretchen dropped her car off at 10AM. She spent 20 minutes walking to the mall, so she arrived at the mall at 10:20AM. She spent an hour and a half browsing the mall, so it is 11:50AM when she finished browsing. She spent 30 minutes eating lunch, so she finished eating at 12:20PM. She spent 20 minutes walking back to the shop to pick up her car, so she picked up her car at 12:40PM.
Upper Elementary:
Question: At the movies, Thomas bought 2 large popcorns for $6 each, a box of candy for $3.50, 2 large drinks for $2.25 each, and an order of nachos for $5.50. If he gave the snack bar attendant $40, how much change will he receive?
Answer: $14.50
Solution: First, we need to find the total amount that Thomas spent. He bought 2 large popcorns for $6 each, so he spent $12 on popcorn. He spent $3.50 on candy. He spent $2.25 on 2 large drinks, so he spent a total of $4.50 on drinks. He spent $5.50 on nachos. In total, he spent $25.50 (12 + 4.50 + 3.50 + 5.50 = 25.50). If he paid $40, then he will receive $14.50 back in change (40 – 25.50 = 14.50).
Middle School:
Question: Four more than twice a number is equivalent to eight less than five times the same number. What is the number?
Answer: 4
Solution: Let x represent the number. If we rewrite the sentence as a mathematical equation, we have:
4 + 2x = 5x – 8
One way to solve this problem is to start by subtracting 2x from both sides.
4 = 3x – 8
Next, let’s add 8 to both sides.
12 = 3x
Divide both sides by 3.
4 = x
The number is 4. We can check our answer by substituting 4 for x.
4 + 2(4) = 5(4) – 8
4 + 8 = 20 – 8
12 = 12
The equation is true, so our answer is 4.
Algebra and Up:
Question: Richard is standing on the top of the second story of a building where each story is 12 feet high. He throws a rope to Kyle and then Kyle walks away from the building until the rope is tight. If Kyle walked 2 1/3 yards away from the building to make the rope tight, how long is the rope, in feet?
Answer: 25 feet
Solution: The shape that is created from the building and the rope is a right triangle, where the legs are the height of the building and how far Kyle walked and the hypotenuse is the length of the rope. In order to compare the sides of the triangle, all of the sides have to be the same unit. Let’s convert all of the sides into feet. Richard is on the top of the second story. For this building, there are 12 feet in one story, so there are 24 feet in two stories. So the height of the building is 24 feet. Kyle walked 2 1/3 yards away from the building. 1 yard is 3 feet, so 2 yards is 6 feet and 1/3 of a yard is 1 foot. So, Kyle walked 7 feet away from the building. So, the legs of the triangle are 7 feet and 24 feet. To find the length of the rope, or the hypotenuse, use the Pythagorean Theorem.
a2 + b2 = c2
Substitute the values for a and b.
72 + 242 = c2
Find the squares of the numbers.
49 + 576 = c2
Simplify the left side.
625 = c2
Take the square root of both sides.
25 = c
The rope is 25 feet long.
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