Answers to Problems of the Week - April 19 to April 24

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: Morgan’s scout troop is having a pizza party. They order 2 each of 3 varieties of pizza, then cut each pizza into 8 slices. How many slices of pizza does Morgan’s scout troop have?

Answer:  48 slices.

Solution:  Morgan orders 2 × 3 = 6 pizzas. If each pizza is cut into 8 slices, that’s 6 × 8 = 48 slices total.

Upper Elementary: 

Question: Lily orders a pizza with black olives on top and cuts it into 4 slices. The first slice has 6 olives. The second slice has 11 olives. The third slice has 7 olives. The last slice has the average number of olives of all the slices.  How many olives are on the last slice?

Answer:  8 olives.

Solution:  To find the average number of olives on the first three slices, first we add 6 + 11 + 7 = 24 olives, then we divide by the 3 slices. That’s an average of 24 ÷ 3 = 8 olives. If we add a slice with 8 olives, that’s a total of 24 + 8 = 32 olives. The average of the 4 slices is still 32 ÷ 4 = 8 olives.

Middle School:

Question: Jessie orders a pizza that costs her $14.50. She tips the pizza delivery person 15% and rounds up to the next dollar. By how much did she round her tip? (Jessie lives in Delaware, where pizza isn’t taxed.)

Answer:  82¢.

Solution:  To find a 15% tip, we multiply: 14.50 × 0.15 = 2.175, which rounds to $2.18. If we round up to the next dollar, we get $3.00, which is 3.00 – 2.18 = .82 or 82¢ more.

Algebra and Up: 

Question: Jack and his family are having a pizza for dinner that weighs 2 pounds. Jack takes a 40° slice. How much does the remaining pizza weigh?

Answer:  1⁷/₉ pounds or about 1.78 pounds.

Solution:  After Jack takes a 40° slice, there are 320° of pizza left. That’s 320 ÷ 360 = ⁸/₉ of the pizza, and ⁸/₉ of 2 pounds is 1⁷/₉ pounds of pizza. 

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

An ant sitting in a ceiling corner of a cube-shaped room notices some honey in the opposite corner on the floor.

The ant may only walk on the walls, floor, and ceiling — no flying or falling — to get the honey.

If the room is 3 meters on each side, what is the length of the shortest path the ant can take?

Answer: 3 * sqrt(5) = 2.236

Solution: