Looking for some fun problems to fill the last days of school?
1. Judy and Dan both collect seashells. 1/3 of Judy’s shells is the same number as 2/5 of Dan’s shells. If they have 88 shells all together, who has more shells? How many more?
2. Ms. Hershey rewards students with a piece of chocolate (approximately 60 calories) for every day that they hand in an assignment. David handed in 7/8 of Ms. Hershey’s assignments over the past school year. Given that 30 minutes of play burns 150 calories, how many assignments did Ms. Hershey assign if it took David 28 hours to burn off all the calories from the chocolates he earned?
3. Three boxes are labeled “Apples”, “Oranges”, and “Apples and Oranges”. Each label is incorrect. You may select only one fruit from one box (no feeling around or peeking permitted). How can you label each box correctly?
4. Danny, Connie, and Jane have eight cookies to share among themselves. They decide that they each do not need to receive the same number of cookies, but each person should receive at least one cookie. If the children do not break any of the cookies, in how many different ways can they share the cookies?
5. Your parents have asked you to choose your own allowance. Allowance Plan A is $5 every day of the month. Allowance Plan B is 1 penny on the first day of the month, 2 pennies on the second day of the month, 4 pennies on the third day of the month, and the amount keeps doubling every day until the month is over. Which plan would you choose? Why? Did your parents make a good choice in offering the two plans? Support your answer with calculations.
6. Who is thirstier, you or your car? What is the volume of gasoline your car uses in a year? How does this compare to the volume of liquid you drink in a year?
7. Given two cylinders, one twice as wide but half as tall as the other, which one holds more?
8. The ratio of Judy’s pens to pencils is 3:4. After she loses a pen and buys two more pencils, the ratio is 2:3. How many pencils did she have in the beginning?
9. The owners of the Riverview Restaurant have hired enough servers to handle 17 tables of customers. The fire marshal has approved the restaurant for 44 customers. How many two-seat tables and how many four-seat tables should the owners purchase?
10. Mr. Bradley discovered that he had accidentally reversed the digits of a test and shorted a student 36 points. Mr. Bradley told the student that the sum of the digits was 14 and agreed to give the student his correct score plus extra credit if he could determine his actual score. What was his actual score on the test?
11. The hospital staff consists of 16 doctors and nurses. There are more nurses than doctors. There are more male doctors than male nurses. There are more male nurses than female nurses. There is at least one female doctor. How many doctors and nurses of each gender make up the hospital staff?
12. A local market buys oranges at 3 for 10 cents and sells them at 5 for 20 cents. How many oranges must it sell in order to make a profit of $1.00?
13. An overnight package delivery service charges $16 for every package safely delivered, but pays a penalty of $48 for every package delivered damaged. If it received $9152 for a delivery of 600 packages, how many packages were safely delivered?
14. Five 5-cm metal cubes and thirteen 2-cm metal cubes were melted and recast into a new metal cube. Find the height of the new metal cube.
15. Let’s make up a new operation whose symbol is ~. The operation is defined as follows: A ~ B = (A + 1) x (B+1). What is the value of 2~3? What is the value of 3~2? Does the operation ~ appear to be commutative? Why or why not?
16. A rectangle and a square have the same perimeter. A side of the square is three times the width of the rectangle, and the length of the rectangle is one more than the side of the square. Find the dimensions of each figure.
17. If a helicopter can fly for 90 minutes on 1 full tank of gas, how many full tanks of gas does it need to fly for 6 hours?
18. What is the product of the quotient and the remainder when 1111 is divided by 22?
19. How many squares of any size are there on a checkerboard?
20. The ratio of Jims’ money to Ed’s money was 7:2. After Jim spent $26 and Ed saved another $14, they each had the same amount of money. How much money did Jim and Ed have altogether at first?
21. If Amy gives 10 of her stamps to Robin, she will have four times as many stamps as Robin. If she gives 20 of her stamps to Robin, She will have three times as many stamps as Robin. How many stamps do they have in all?
22. The University has space in its freshman class for 3,835 students. If 65% of the students who are admitted will actually attend, how many students should the university admit?
23. Julian wants to build a fence around his circular garden. The garden measures 10 yards from side to side across the middle. The fencing material costs $5 per foot. Julian has a part time job for which he earns $13 per hour. How many hours will he have to work in order to pay for the fence?
24. How many M&M’s would fit in a line from Richmond, VA to Sacramento, CA?
25. To accurately measure the radius of a spherical rock, you place the rock in a cylindrical glass containing water. When you do so, the water level rises 9/64 inches. The radius of the glass is 2 inches. What is the radius of the rock?
26. Sandy is taking a cab in New York City. The taxi fare includes a base charge of $2.50 as soon as you enter the cab, plus an additional $2.50 per mile traveled. If Sandy starts off with a $20 bill, takes the cab for 5.7 miles, and leaves a $2.75 tip, will she have enough money left to buy a bag of M&M’s for 65 cents?
27. Dr. Simon was performing a chemistry experiment. She needed exactly 17.031 mg of acid. She had 4.85 mg left from her last experiment, and four new bottles of acid with 2.85 mg in each. Does Dr. Simon have enough? If she has enough, how much will she have left after this experiment? If she doesn’t have enough, how much more does she need?
28. Alice has 50% of the amount of money Betty has, and Carrie has 2/5 of what Alice has. If Betty has $364 more than Carrie, how much money does Alice have?
29. Abe, Barry, and Carlos have 256 marbles altogether. The ratio of Abe’s marbles to Barry’s marbles is 4 : 3. Barry has 14 more marbles than Carlos. How many marbles does Abe have?
30. Two women, Alice and Carol, and two men, Brian and David, are athletes. One is a swimmer, a second is a skater, a third is a gymnast, and a fourth is a tennis player. On a day they seated around a square table. The swimmer sat on Alice’s left. The gymnast sat across from Brian. Carol and David sat next to each other. A woman sat on the skater’s left. Who is the tennis player?
31. Callie and her friend Chris are trying to use a calculator to solve 88 x 8. However, when Callie got out her calculator, she noticed that it had two broken keys. Both the 8 key and the x key were broken! Chris suggested that if they changed the numbers in the problem and did not use the x key, they could still use the broken calculator to find the answer. Is Chris right? Find a way for Callie and Chris to use other keys on the broken calculator to solve 88 x 8. Explain why your methods work.
32. A shopkeeper bought 9 boxes of 84 peaches at $17 per box. He sold 300 peaches at 4 for $1 and the remaining peaches at 3 for $1. What was his total profit?
33. The ratio of the amount of Robert’s money to that of Jasmine’s is 4:11. The ratio of the amount of Morgan’s money to that of Jasmine’s is 5:6. If Robert and Jasmine have $36 altogether, how much more money does Morgan have than Robert?
34. What fraction of the area of your city is covered by automobiles?
35. Aryabhata, a sixth century Hindu mathematician, wrote: “Add 4 to 100, multiply by 8, and then add 62,000; the result is approximately the circumference of a circle of 20,000. By this rule the relation of the circumference to diameter is given.” What value of pi do you derive from Arybhata’s rule?
36. At Mrs. Ong’s shop, there were two vases for sale at $630 each. She sold one of them at this price and earned 40 percent of what she paid for it. She sold the other vase later at a 20 percent discount. If the two vases had the same costs, how much did Mrs. Ong earn altogether?
37. Use 16 base ten blocks to represent a number. What numbers can you represent?
38. Lee and Chan drove from Town P to Town Q. They started their journeys at different times. Lee drove at an average speed of 45 km/h and took 40 min. Chan drove at an average speed of 72 km/h and reached Town Q at the same time as Lee. How far was Town P from Town Q? How many minutes later than Lee did Chan start his journey?
39. Assign each letter of the alphabet a number value starting with A. Your code will be as follows: A is 1, B is 2, C is 3, D is 4, and so on. Z is last and is 26. How many words can you find that are worth 100?
40. Three days before the day after tomorrow is Monday. What day is today?
41. If it takes 6 men working 6 hours each to dig a hole in the ground, then how long will it take 1 man to dig 1/2 hole?
42. On his last test, Kyle scored a 95, raising his average by 1 point to 89. What must he score on his next test to raise his average to 90?
43. Which number is larger, the product of the multiples of 5 that are between 7 and 37 or the product of the multiples of 6 that are between 7 and 37?
44. When a positive number is divided by its reciprocal, the result is 4/9. What is the number?
45. When the nine justices of the Supreme Court meet, they greet one another with a handshake to show harmony of purpose, even though their views may differ. How many handshakes occur? In general, how many handshakes occur when there are n people?
46. If Alex sells his computer for $2392, he makes a profit of 30%. What price should he charge if he wants a profit of 40%?
47. Darcy likes to eat apple slices with peanut butter and raisins. On each apple slice she puts 1/16 cup of peanut butter and 8 raisins. Today Darcy has 3/8 cup of peanut butter and 80 raisins. She eats apple slices until the peanut butter is all gone. What fraction of the 80 raisins did she eat?
48. If 2/3 of a lawn takes 3/4 of an hour, how much can I mow in one hour?
49. Would you rather have a stack of quarters from the floor to the top of your head or $200?
50. A movie theater has 40 rows of chairs. The first row has 10 chairs and each additional row has 2 more chairs than the row before it. Our school has 1800 students and 100 teachers. Are there enough seats in the theater for all of our students and teachers?