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March Problems of the Month

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This document contains summaries of 14 math word problems from March 2013. The problems cover a range of math topics including probability, statistics, geometry, number theory, and algebra. Sample problems include finding the average speed in a multi-part bicycle race, determining possible numbers of candy pieces in a bag, and calculating the cost of a song on a new music website.

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March Problem Solving Modeling with Mathematics (MP4) adapted from MTMS Feb 2013 & Dec 2013
3/1/13 Whats Your Favorite? A company surveyed students about their favorite flavors of ice cream. Of those students surveyed, at least 1 was a girl and more than 93% were boys. What is the smallest possible number of students in the survey?
3/4/13 A Prime Example What is the smallest three-digit prime number whose digits are also prime?
3/5/13 Pedal Faster! In a 20-mile bicycle race, Matthew went twice as fast as Tim, and Sally went twice as fast as Matthew. Sally finished 3.75 hours ahead of Tim. What was Matthews average speed (in miles per hour) for the race?
3/6/13 Make a Prediction! If the letters in the following sequence are repeated indefinitely, what is the 2000th letter in this pattern? HIGHSCHOOLMATHEMATICSHIGHSC
3/7/13 Sweet Tooth Mr. Zucker has a bag of candy containing less than 100 pieces, which he will distribute to the class. If he makes groups with 2, 3, or 4 pieces of candy, he will have 1 piece leftover in the bag. If he makes groups with 5 pieces of candy, he will have no candy left in the bag. How many pieces of candy could be in Mr. Zuckers bag? List all possibilities.
3/8/13 Fun with Fractions A unit fraction, such as 1/2, 1/11, and 1/25, is a fraction in the form of 1/n, where n is a positive integer. Find a pair of unit fractions such that their difference is 1/72.
3/11/13 A Power-full Problem Observe the following set that contains 26 powers of three: 30, 31, 32, 33, . . . , 325 How many numbers in the set will have a units digit (ones digit) of 1?
3/12/13 Get the Best Deal! Bobs Furniture is running a promotion. Any purchase less than $4500 receives a 10% discount; a purchase of $4500 or more receives a 20% discount. Katie has determined that it is actually cheaper to buy more merchandise and bring her bill up to $4500 to obtain the 20% discount. Under what circumstances will this be true?
3/13/13 An Age-Old Problem When asked his age, Ryan said, My age is a number between 30 and 60, the difference between the digits is 4, and the mean of the digits is 6. How old is Ryan?
3/14/13 I Pledge to Solve This Problem Shane is standing next to the schools flagpole. He notices that the flagpoles shadow from the sun extends across 3 full sections of sidewalk (all the same size), and that his shadow only extends across 3/4 section of a side-walk. If Shane is 6 ft. 2 in. tall, how tall is the flagpole?
3/15/13 Turn up the Volume A new website called MyTunes.com charges for songs on the basis of the length of each song. Deriving Me Crazy is 3 minutes, 36 seconds long and costs $1.08. Tessellate My Heart is 2 minutes, 44 seconds long and costs $0.82. How much would MyTunes.com charge for Polygon Forever, which is 3 minutes, 12 seconds long?
3/18/13 Mean, Median, Mode! License plate numbers issued in Norfolk County contain 6 digits, each in the range of 09. For the 6 digits of Deannas license plate, the range is 9, the mean is 4.5, the median is 5.5, and the mode is 6. What are the 6 digits on Deannas license plate?
3/19/13 A Statistical Situation A set of 5 different positive integers has a mean of 33 and a median of 40. Within this set, how large can the greatest number be?
3/20/13 1, 2, 3, 4, 5, 6, 7, 8, .. To play the math game Bizz Buzz, you begin counting at 1 but skip all multiples of 3 and 5 and all numbers that contain the digits 3 and 5. In this game, the number 16 is the 8th number. If you continue this game, what is the 25th number?
3/21/13 Lots of Options! Students at a school picnic can choose either a hamburger or a hot dog and can choose among ketchup, mustard, and cheese for toppings. If students can have all, some, or none of the toppings, how many different sandwiches can be made?
3/22/13 If -11 is the output, whats the input? If -11 is the output, whats the input? In each pair of numbers below, the input is the first number and the output is the second number. After examining the five input and output pairs below, determine the output if the input is 11. (1, 3) (0, 6) (2, 12) (10, 36) (97, 297)
3/25/13 Which number doesnt belong? Of the following 10 numbers, one is unlike the other 9 numbers. Which number does not belong in this 10-number set? Hint: Consider multiplication. {6, 15, 39, 65, 77, 95, 105, 133, 221, 437}
3/26/13 Rolling the Dice Two dice are rolled. What is the probability that the numbers on the dice will be consecutive?
3/27/13 Who Am I? I am a number. I am the sum of the measures of the interior angles of a triangle, divided by the number of sides in a dodecagon, multiplied by the most frequently occurring digit in the first 5 numbers in the sequence 1, 4, 16, . . . , and less the median of those same 5 numbers. What number am I?
3/28/13 Minty Fresh The Bits o Mints Company sells tins that contain 24 cylindrical mints that are 1 cm wide and 1/2 cm tall. The mints are arranged 4 wide, 3 deep, and 2 high and fit snugly in their rectangular prism tin. How many cubic centimeters of space in the tin are empty?
3/29/13 A Geometric Probability Problem Joels living room wall is 13 feet long with 2-inch wide vertical support beams every 16 inches, starting at the right edge of the wall. If Joel wants to hang a mirror that is right edge of the wall. If Joel wants to hang a mirror that is secured to one of the support beams, what are the chances that a randomly placed nail will go through a beam?
Doing Good Deeds Bobby was inspired to do good deeds in his community. The first day, he did 1 good deed for 2 neighbors. When they asked how to repay him, he told them to do 2 good deeds for 2 other people the next day. each neighbor complied. Bobby repeated what he did the first day. After how many days would 1000 good deeds have been done?

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March Problems of the Month

  • 1. March Problem Solving Modeling with Mathematics (MP4) adapted from MTMS Feb 2013 & Dec 2013
  • 2. 3/1/13 Whats Your Favorite? A company surveyed students about their favorite flavors of ice cream. Of those students surveyed, at least 1 was a girl and more than 93% were boys. What is the smallest possible number of students in the survey?
  • 3. 3/4/13 A Prime Example What is the smallest three-digit prime number whose digits are also prime?
  • 4. 3/5/13 Pedal Faster! In a 20-mile bicycle race, Matthew went twice as fast as Tim, and Sally went twice as fast as Matthew. Sally finished 3.75 hours ahead of Tim. What was Matthews average speed (in miles per hour) for the race?
  • 5. 3/6/13 Make a Prediction! If the letters in the following sequence are repeated indefinitely, what is the 2000th letter in this pattern? HIGHSCHOOLMATHEMATICSHIGHSC
  • 6. 3/7/13 Sweet Tooth Mr. Zucker has a bag of candy containing less than 100 pieces, which he will distribute to the class. If he makes groups with 2, 3, or 4 pieces of candy, he will have 1 piece leftover in the bag. If he makes groups with 5 pieces of candy, he will have no candy left in the bag. How many pieces of candy could be in Mr. Zuckers bag? List all possibilities.
  • 7. 3/8/13 Fun with Fractions A unit fraction, such as 1/2, 1/11, and 1/25, is a fraction in the form of 1/n, where n is a positive integer. Find a pair of unit fractions such that their difference is 1/72.
  • 8. 3/11/13 A Power-full Problem Observe the following set that contains 26 powers of three: 30, 31, 32, 33, . . . , 325 How many numbers in the set will have a units digit (ones digit) of 1?
  • 9. 3/12/13 Get the Best Deal! Bobs Furniture is running a promotion. Any purchase less than $4500 receives a 10% discount; a purchase of $4500 or more receives a 20% discount. Katie has determined that it is actually cheaper to buy more merchandise and bring her bill up to $4500 to obtain the 20% discount. Under what circumstances will this be true?
  • 10. 3/13/13 An Age-Old Problem When asked his age, Ryan said, My age is a number between 30 and 60, the difference between the digits is 4, and the mean of the digits is 6. How old is Ryan?
  • 11. 3/14/13 I Pledge to Solve This Problem Shane is standing next to the schools flagpole. He notices that the flagpoles shadow from the sun extends across 3 full sections of sidewalk (all the same size), and that his shadow only extends across 3/4 section of a side-walk. If Shane is 6 ft. 2 in. tall, how tall is the flagpole?
  • 12. 3/15/13 Turn up the Volume A new website called MyTunes.com charges for songs on the basis of the length of each song. Deriving Me Crazy is 3 minutes, 36 seconds long and costs $1.08. Tessellate My Heart is 2 minutes, 44 seconds long and costs $0.82. How much would MyTunes.com charge for Polygon Forever, which is 3 minutes, 12 seconds long?
  • 13. 3/18/13 Mean, Median, Mode! License plate numbers issued in Norfolk County contain 6 digits, each in the range of 09. For the 6 digits of Deannas license plate, the range is 9, the mean is 4.5, the median is 5.5, and the mode is 6. What are the 6 digits on Deannas license plate?
  • 14. 3/19/13 A Statistical Situation A set of 5 different positive integers has a mean of 33 and a median of 40. Within this set, how large can the greatest number be?
  • 15. 3/20/13 1, 2, 3, 4, 5, 6, 7, 8, .. To play the math game Bizz Buzz, you begin counting at 1 but skip all multiples of 3 and 5 and all numbers that contain the digits 3 and 5. In this game, the number 16 is the 8th number. If you continue this game, what is the 25th number?
  • 16. 3/21/13 Lots of Options! Students at a school picnic can choose either a hamburger or a hot dog and can choose among ketchup, mustard, and cheese for toppings. If students can have all, some, or none of the toppings, how many different sandwiches can be made?
  • 17. 3/22/13 If -11 is the output, whats the input? If -11 is the output, whats the input? In each pair of numbers below, the input is the first number and the output is the second number. After examining the five input and output pairs below, determine the output if the input is 11. (1, 3) (0, 6) (2, 12) (10, 36) (97, 297)
  • 18. 3/25/13 Which number doesnt belong? Of the following 10 numbers, one is unlike the other 9 numbers. Which number does not belong in this 10-number set? Hint: Consider multiplication. {6, 15, 39, 65, 77, 95, 105, 133, 221, 437}
  • 19. 3/26/13 Rolling the Dice Two dice are rolled. What is the probability that the numbers on the dice will be consecutive?
  • 20. 3/27/13 Who Am I? I am a number. I am the sum of the measures of the interior angles of a triangle, divided by the number of sides in a dodecagon, multiplied by the most frequently occurring digit in the first 5 numbers in the sequence 1, 4, 16, . . . , and less the median of those same 5 numbers. What number am I?
  • 21. 3/28/13 Minty Fresh The Bits o Mints Company sells tins that contain 24 cylindrical mints that are 1 cm wide and 1/2 cm tall. The mints are arranged 4 wide, 3 deep, and 2 high and fit snugly in their rectangular prism tin. How many cubic centimeters of space in the tin are empty?
  • 22. 3/29/13 A Geometric Probability Problem Joels living room wall is 13 feet long with 2-inch wide vertical support beams every 16 inches, starting at the right edge of the wall. If Joel wants to hang a mirror that is right edge of the wall. If Joel wants to hang a mirror that is secured to one of the support beams, what are the chances that a randomly placed nail will go through a beam?
  • 23. Doing Good Deeds Bobby was inspired to do good deeds in his community. The first day, he did 1 good deed for 2 neighbors. When they asked how to repay him, he told them to do 2 good deeds for 2 other people the next day. each neighbor complied. Bobby repeated what he did the first day. After how many days would 1000 good deeds have been done?