Lower Elementary
Question: Rachel runs for 20 minutes every day. If she runs 1 mile in 10 minutes, how many miles will she have ran in 3 days?
Answer: 6 miles
Solution: Rachel runs 20 minutes every day. Because she runs 1 mile every 10 minutes, she runs 2 miles in 20 minutes, so she runs 2 miles every day. In 3 days she will run 6 miles (2 + 2 + 2).
Upper Elementary
Question: A certain crane can lift a maximum load of 25,234 pounds. The Incredible Hulk can lift double the maximum weight the crane lifts. How much can the Hulk lift?
Answer: 50,468
Solution: There are a number of ways to approach this problem. One way is to use the Mathnasium method for doubling.
Double 25,234 = Double 20,000 + Double 5,000 + Double 200 + Double 30 + Double 4 = 50,468 pounds
Students can also add 25,234 to itself or multiply 25,234 by 2 to obtain the answer.
Middle School
Question: A salesman made $2,050 last month which includes both his salary and his commission. If he makes 5% commission on all of his sales and earns a monthly salary of $1,600, what was the dollar amount of his sales last month?
Answer: $9,000
Solution: The salesman only makes commission on what he sold. By subtracting his salary, $1,600, from his total revenue last month, we are left with the amount of money he made from commission.
$2,050 – $1,600 = $450
This tells us that 5% of his sales last month is equal to $735. Let s be the dollar amount of his sales last month,
.05(s) = $450
Solve for s.
s = $450/.05 = $9,000
Using the Mathnasium method for percentages (percent means “for each 100”) another way of solving this problem is as follows.
How many times do you have to count 5 to make 450? (90 times)
Since you have to count 5, 90 times to make 450 and each count represents a hundred, 90 hundreds equal 9,000.
Algebra and Up
Question: Two fishing boats left the same harbor at the same time. Boat A traveled northwest for 3 hours at 20 knots to a fishing spot. Boat B traveled northeast for 4½ hours at 14 knots to another fishing spot. How far apart are the two fishing spots? (Note: 1 knot ≈ 1.15 mph)
Answer: 100.05 miles
Solution: Because Boat A is traveling northwest and Boat B is traveling northeast, they form a 90Ëš angle from the harbor. First convert knots to miles per hour, then finding how far the two boats traveled. We can use the Pythagorean Theorem to solve for the distance between the two fishing spots.
Boat A:
20 knots • 1.15mph/knot = 23 mph
23 mph • 3 hours = 69 miles
Boat B:
14 knots • 1.15mph/knot = 16.1 mph
16.1 mph • 4.5 hours = 72.45 miles
Using the Pythagorean Theorem:
a2 + b2 = c2
c = √(692 + 75.452) = 100.05 miles
