Challenging Math Problems: Weight, Nuts, Speed, Time, Angles, Pizza

1. Question 1 - Group Dr. Jekyll has made a monstrous blob that is growing at an alarming rate.  At the time of creation it weighed 1 pound, an hour later it weighed 7 pounds, and an hour after that it weighed 25 pounds.  He thought the growth would begin to slow, but an hour later it was 61 pounds and an hour after that it grew to 121 pounds.  At this point the doctor is concerned.  Dr. Jekyll believes that he can contain the growth, but only if he can figure out how much the monstrous blob will weigh next.  Assuming the pattern continues, how much will the blob weigh at the end of the next hour?

2. Question 1 Answer At the time of creation it weighed 1 pound, an hour later it weighed 7 pounds, and an hour after that it weighed 25 pounds.  He thought the growth would begin to slow, but an hour later it was 61 pounds and an hour after that it grew to 121 pounds. Solution: 1, 7, 25, 61, 121 ____ 6 18 36 60 90 12 18 24 30 6 6 6 211

3. Question 2 As winter approaches, Sandy Cheeks begins to gather nuts. The average chipmunk gathers 32 nutshells in 3 days. Unfortunately, 1 out of every 8 nutshells is hollow and does not contain a nut. How many nuts can 3 chipmunks expect to gather in 2 weeks, assuming that 1 out of every 8 nutshells is empty.

4. Question 2 Answer As winter approaches, Sandy Cheeks begins to gather nuts. The average chipmunk gathers 32 nutshells in 3 days. Unfortunately, 1 out of every 8 nutshells is hollow and does not contain a nut. How many nuts can 3 chipmunks expect to gather in 2 weeks, assuming that 1 out of every 8 nutshells is empty. Solution: 1 chipmunk = 32 – 4 = 28 nuts in 3 days 28/3 x 3 x 14 =…… 392 nuts

5. Question 3 Professor Severus Snape spots Harry Potter speeding on his broom and clocks it at 80 miles per hour. Snape flies after Harry ½ mile behind. If the professor travels at an average speed of 100 miles per hour, exactly how many minutes will it take for him to overtake Harry?

6. Question 3 Answer Professor Severus Snape spots Harry Potter speeding on his broom and clocks it at 80 miles per hour. Snape flies after Harry ½ mile behind. If the professor travels at an average speed of 100 miles per hour, exactly how many minutes will it take for him to overtake Harry? Solution: Snape has to catch up ½ a mile, but relative to Harry he is only going 20 mph. 20 mph is 1 mile every 3 minutes so going ½ a mile would take…. 1.5 minutes

7. Question 4 A group of bands got together to prepare for a huge combined number at the Grammy Awards. The day didn’t go as planned.  One Direction wasted 1/3 of the time telling Katie Perry“What Makes You Beautiful.”  Then Jessie J spent ¼ of the remaining time arguing with the pizza deliveryman about the “Price Tag” on their lunch.  After eating, One Republic didn’t want to work, so they spent 1/5 of the remaining time telling “Secrets” in the corner.  That left the group only 4 hours to work before Taio Cruz got so mad he started playing with “Dynamite” and blew up the studio at 7:00 PM! What time did they start working?

8. Question 4 Answer What time did they start working? Working backwards…. Using 1/5 of the time telling secrets left 4/5 of the time remaining time which was 4 hours, so before telling secrets they had 5 hours. Continuing with that logic algebraically… 4/5x = 4 x = 5 3/4x = 5 x = 20/3 2/3x = 20/3 x = 10 9 am 10 hours before 7pm is…

9. Question 5 Equilateral triangle TOP rests on top of square TOWN. Segment TO is one diagonal of the entire figure, POWNT. Draw the other diagonals of figure POWNT. What is the measure of angle PWO?

10. Question 5 Answer Equilateral triangle TOP rests on top of square TOWN. What is the measure of angle PWO? Solution: Angle POW = 90 + 60 = 150 degrees 180 – 150 = 30 degrees Therefore angle PWO is 15 degrees

11. Question 6 - Group Mario and Luigi are having a pizza-making contest. Since Luigi is the older brother and does most of the shopping, he has the 1½ cups of shredded cheese needed to bake the perfect twelve-inch diameter pizza. Mario, however, has only 1¼ cups of shredded cheese. What diameter pizza, to the nearest hundredth of an inch, should Mario make so that the 1 ¼ cups of cheese will make his pizza taste as “cheesy” as Luigi’s 12-inch pizza with the 1½ cups cheese? Helpful tip: A = πr2

12. Question 6 Answer Mario and Luigi are having a pizza-making contest. Since Luigi is the older brother and does most of the shopping, he has the 1½ cups of shredded cheese needed to bake the perfect twelve-inch diameter pizza. Mario, however, has only 1¼ cups of shredded cheese. What diameter pizza, to the nearest hundredth of an inch, should Mario make so that the 1 ¼ cups of cheese will make his pizza taste as “cheesy” as Luigi’s 12-inch pizza with the 1½ cups cheese? Helpful tip: A = πr2 Solution: Solving the proportion gives you a radius of approximately 5.47722558 inches. Multiply that by 2 to get a diameter of… 10.95 inches

13. Question 7 Tired of grading math tests, Sara and Matt’s math teacher threw the entire stack of papers down the stairs.  There are 24 steps on the stairs and the math tests fell randomly on the steps in a way that they were equally likely to land on any step.  She gave A’s to the papers that landed on the bottom 6 steps, B’s to papers that landed on the next 4 steps, C’s to papers that landed on the next 10 steps, and D’s to papers that landed on the top 4 steps.  She didn’t fail anybody – how nice!  What is the probability, rounded to the nearest whole percent, that Sara gets an A and Matt gets a B?

14. Question 7 Answer Tired of grading math tests, Sara and Matt’s math teacher threw the entire stack of papers down the stairs.  There are 24 steps on the stairs and the math tests fell randomly on the steps in a way that they were equally likely to land on any step.  She gave A’s to the papers that landed on the bottom 6 steps, B’s to papers that landed on the next 4 steps, C’s to papers that landed on the next 10 steps, and D’s to papers that landed on the top 4 steps.  She didn’t fail anybody – how nice!  What is the probability, rounded to the nearest whole percent, that Sara gets an A and Matt gets a B? Solution: Which is…. 4 percent

15. Question 8 A farmer found that his cow and goat would eat all the grass in a certain field in 45 days, that his cow and goose would eat it in 60 days, but that it would take his goat and goose 90 days to eat it all. If he turns the cow, the goat, and the goose loose in the field together, how long will it take them to eat all the grass? Assume that the grass is not growing each day.

16. Question 8 Answer A farmer found that his cow and goat would eat all the grass in a certain field in 45 days, that his cow and goose would eat it in 60 days, but that it would take his goat and goose 90 days to eat it all. If he turns the cow, the goat, and the goose loose in the field together, how long will it take them to eat all the grass? Assume that the grass is not growing each day. Solution: 2c + 2g + 2t = 2c + 2g + 2t = 9/180 = 1/20 Dividing by 2 yields c + g + t = 1/40 therefore it will take the three of them… 40 days

17. Question 9 If two sides of a square field are increased by three feet, as shown in the diagram, the area of the field would increase by 129 square feet. Find the area of the original field.

18. Question 9 Answer If two sides of a square field are increased by three feet, as shown in the diagram, the area of the field would increase by 129 square feet. Find the area of the original field. Solution: If the sides of the square are x, the the area the field increased by is 3x + 3x + 9. The total area in that new portion is 129 square feet so solving 3x + 3x + 9 = 129 gives us that x is 20 feet so the area is… x x 400 square feet

19. Question 10 A man bought some plates. 2/3 of them were cracked, ½ of them were chipped, and ¼ of them were both chipped and cracked. All but two of the plates were either chipped or cracked or both. How many plates did he buy?

20. Question 10 Answer A man bought some plates. 2/3 of them were cracked, ½ of them were chipped, and ¼ of them were both chipped and cracked. All but two of the plates were either chipped or cracked or both. How many plates did he buy? Solution: so 11/12 of the plates are either chipped cracked or both. Add 2 to that to find the total giving the equation… 24 plates