Lower Elementary:
Question: Brittany brought a cake to school to share with her 13 classmates. If the cake was cut into 20 pieces and every student and the teacher had a piece of cake, how many pieces were left over?
Answer: 5 pieces left
Solution: Because Brittany is sharing with her classmates we assume she is one of the students having a piece of cake. All 14 students (13 classmates and Brittany) and the teacher had a piece of cake. So a total of 15 people had a piece of cake. To find how many pieces left over, we subtract 15 from 20.
20 pieces – 15 pieces = 5 pieces
Upper Elementary:
Question: Cameron collects baseball cards. Unfortunately Cameron lost half of his cards, but after searching for them he found half of the cards he lost. If Cameron had 128 before he lost any, how many cards does he have now?
Answer: 96 cards
Solution: Cameron lost half of his 128 baseball cards.
Half of 128 = half of 100 + half of 20 + half of 8 = 50 +10 + 4 = 64
After losing 64 cards, Cameron is left with only 64 cards, but then he found half of the cards he lost.
Half of 64 = half of 60 + half of 4 = 30 + 2 = 32
He had 64 cards and found 32. To find the total number of cards he has, we add 64 and 32.
64 + 32 = 96
Middle School:
Question: The Bugatti Veyron Super Sport is the fastest production car in the world with a top speed of 267mph. At that speed the 26.4 gallon gas tank will run out in 12 minutes. How many miles per gallon does the Bugatti Veyron get at its top speed?
Answer: About 2.02 miles/gal
Solution: Because we know that it takes 12 minutes to deplete the 26.4 gallon gas tank, we can find how much gas the Veyron uses every minute by dividing 26.4 gallons by 12 minutes.
24.6 gal ÷ 12 min = 2.2 gal/minute
Now we find how far the Veyron travels in a single minute. We do this by converting 267 miles/hour into miles/min.
267 miles/hour â— 1/60 hours/minute = 4.45 miles/min
Finally we divide 4.45 miles/min by 2.2 gal/min.
4.45 miles/min ÷ 2.2 gal/min = 2.02 miles/gal
Algebra and Up:
Question: In the figure below one square is concentric with another larger square. Find the area of the shaded region. *Concentric means they share the same center.
Answer: 250 units2
Solution: Start by drawing another line from the center to the bottom right corner, which will complete a special 45-45-90 triangle.
In a 45-45-90 triangle the hypotenuse is √2 times larger than the legs. The hypotenuses of the triangles are also the sides of the squares. The side of the small square is 10√2 units and the side of the larger square is 15√2 units.
In order to find the area of the shaded region (the part) we must first find the area of the larger square (the whole) and subtract the smaller square (the other part).
AS = s2 = (10√2 units)2 = 200 units2
AB = s2 = (15√2 units)2 = 450 units2
Ashaded = AB – AS = 450 units2 – 200 units2 = 250 units2
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