Answers to Problems of the Week - November 23 to November 28

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up.

Lower Elementary:

Question: Chloe had an excellent fishing day. She caught 6 snappers, 4 mackerels, 1 grouper, and 1 soggy boot. She threw half the snappers and half the mackerels back into the ocean. How many fish did she take home?

Answer:  6 fish

Solution:  Chloe caught 6 + 4 + 1 = 11 fish in total. She threw 3 snappers back because half of 6 is 3, and she also threw 2 mackerels back because half of 4 is 2. That means she went home with 11 – 3 – 2 = 6 fish.

Upper Elementary:

Question: Landon goes to a theme park where ride tokens cost 25¢. A roller coaster ride takes 3 tokens. A ride on the Ferris wheel takes 5 tokens. Landon rides the roller coaster and the Ferris wheel 7 times each. How much money did Landon spend on rides?

Answer:  $14.00

Solution:  Three tokens for the roller coaster cost 25¢ × 3 = 75¢. Five tokens for the Ferris wheel cost 25¢ × 5 = $1.25. The total cost for 7 rides on the roller coaster cost $0.75 × 7 = $5.25, and 7 rides on the Ferris wheel cost $1.25 × 7 = $8.75. So, Landon spent $5.25 + $8.75 = $14.00 on rides.

Middle School:

Question: A hamster and a guinea pig are running on wheels. The hamster’s wheel is 6 inches in diameter. The guinea pig’s wheel is 18 inches in diameter. How much farther does the guinea pig run for each rotation of its wheel?

Answer:  12π inches

Solution:  The formula we use to find the circumference of a circle is C = πd, d being the diameter of the circle. The hamster runs π × 6 = 6π inches. The guinea pig runs π × 18 = 18π. So, the guinea pig runs 18π – 6π = 12π inches farther than the hamster.

Algebra and Up:

Question: It costs $20.00 to rent a jet ski, plus $1.50 for each hour of use, plus the cost of gas. James rents a jet ski for 2 hours. He uses 3 quarts of gas, which costs $2.98 per gallon. How much did the jet ski rental cost altogether?

Answer:  $25.24

Solution:  To find the price of the rentals, we can use the expression C = $20.00 + $1.50t + $2.98g wherein C is the total cost of the rental, t is the number of hours spent with the jet skis, and g is the gallons of gas used. James rented 1 jet ski for 2 hours and used 0.75 gallons of gas, so he spent $20.00 + $1.50 × 2 + $2.98 × 0.75 = $25.24 after rounding.

Challenge problem to take home. 20 points for the correct answer. 

The map of Ellie’s newspaper route below shows all of the houses (the vertices) and the paths between them (the edges), as well as the number of pieces of candy on each path.

What is the most candy Ellie can pick up without ever retracing her steps while delivering every house its newspaper? Assume that Ellie can start her route at any house, but she cannot teleport.

Answer: 84 pieces