Lower Elementary
Question: Jeremy bought a sandwich for $4.00, a drink for $1.50, and chips for $1.00. Lola bought the same sandwich and a drink, but instead of buying chips she bought a cookie. If Lola’s whole meal costs her $6.00, how much did she pay for the cookie?
Answer: 50¢
Solution: Lola bought a sandwich, a drink, and a cookie for $6.00. The sandwich costs $4.00 and a drink costs $1.50. Because the whole cost is equal to the sandwich cost plus the drink cost plus the cookie cost, by subtracting the sandwich cost and the drink cost from the whole cost leaves us with the cookie cost.
$6.00 –$4.00 – $1.50 = $0.50 = 50¢
Upper Elementary
Question: A certain elephant weighs 172 pounds more than 9 times the weight of a Honda Civic. If a Honda Civic weighs 2608 pounds, how much does this elephant weigh?
Answer: 23644 pounds
Solution: Because a Honda Civic weighs 2608 pounds, an elephant weighs 172 pounds more than 9 times 2608.
9 times the weight of a Honda Civic:
9 × 2608 = 23472
172 pounds more than 9 times the weight of a Honda Civic:
23472 + 172 = 23644
Middle School
Question: The iPad 2 has a screen resolution of 1024×768 and the new iPad 3’s screen resolution is double that of the iPad2. If the screen on both the iPad 2 and the iPad 3 are 5.8 inches wide and 7.8 inches tall, how many more pixels per square inch does the iPad 3 have than the iPad 2? Round your answer to the nearest pixel.
Answer: About 52150 pixels more per square inch
Solution: Doubling the resolution of the iPad 2 gives us the resolution of the iPad 3 at 2048×1536. This means that the screen iPad 3 there are 3145728 pixels (2048 × 1536) and the screen of the iPad 2 has 786432 pixels (1024 × 768). Because the screens of both iPads are 5.8 inches by 7.8 inches, the area of the screen is 45.24 square inches. Dividing the total pixels of each iPad by screen’s area will give the number of pixels per square inch for each iPad.
iPad 2:
786432 pixels ÷ 45.24 square inches ≈ 17,384 pixels per square inch
iPad 3:
3145728 pixels ÷ 45.24 square inches ≈ 69,534 pixels per square inch
Subtracting the number of pixels per square inch of the iPad 2 from the iPad 3 gives us our final answer.
69,534 – 17,384 = 52150
Algebra and Up
Question: Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find all three integers.
Answer: 20, 22, 24
Solution: Let n be the first of the three consecutive even integers. Then these three consecutive integers can be written in the form of:
n, n+2, n+4
Rewriting the question in algebraic form,
n + 3(n + 2) = 38 + 2(n + 4)
Solving for n,
n + 3n + 6 = 38 + 2n + 8
4n + 6 = 2n + 46
2n = 40
n = 20
Because n = 20, the three consecutive even integers are 20, 22, and 24.
