Algebra, Word Problems

Word problems present mathematical challenges in a narrative or real-world context. Solving them requires translating the text into mathematical equations or expressions and then applying appropriate mathematical techniques. These can span arithmetic, algebra, geometry, etc.

• The Truth-Teller and Liar Survey

  13 truth-tellers and 12 liars participated in a survey. In the survey, each participant was asked about every other participant (including themselves) whether they were a truth-teller. How many "yes" answers were received in the survey in total?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 2

• The Orange Path

  In the illustration, there is an orange path surrounding a blue square. The area of the path is 44% of the area of the square.
  What is the width of the orange path as a percentage relative to the side length of the blue square?

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems Arithmetic -> Percentages
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 3

• Consecutive Numbers and Deletion

  Yossi wrote 10 consecutive natural numbers on the board. Danny erased one of the numbers. The sum of the remaining numbers on the board is 2020.
  Which number was erased?

  Topics:

  Algebra -> Word Problems Algebra -> Sequences Arithmetic -> Division with Remainder
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 5

• Mathematical Conference

  202 participants from three countries attended a mathematical conference: Israel, Greece, and Japan.
  On the first day, every pair of participants from the same country shook hands. On the second day, every pair of participants
  where one was Israeli and the other was not Israeli shook hands. On the third day, every pair of participants where one
  was Israeli and the other was Greek shook hands. In total, 20200 handshakes occurred. How many
  Israeli participants were at the conference?

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  Topics:

  Number Theory Combinatorics Algebra -> Word Problems Algebra -> Equations -> Diophantine Equations
  Sources:
  • Gillis Mathematical Olympiad, 2019-2020 Question 2

• Children's Clubs

  In a kindergarten, there are three clubs: Judo, Agriculture, and Mathematics. Each child participates in exactly one club, and each club has at least one participant. The total number of children in the kindergarten is 32. On Friday, the kindergarten teacher gathered 6 children to tidy up the classroom. The teacher counted and found that exactly half of the Judo club members, a quarter of the Agriculture club members, and an eighth of the Mathematics club members volunteered for the task. How many students are in each club?

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  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Arithmetic -> Fractions Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division
  Sources:
  • Gillis Mathematical Olympiad, 2018-2019 Question 1

• Shuki's Walk

  Shuki walked for 3.5 hours. In every one-hour period, he walked 5 km. Does this mean that Shuki's average speed during the time he walked is 5 km/h?

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  Topics:

  Algebra -> Word Problems Algebra -> Inequalities -> Averages / Means
  Sources:
  • Tournament of Towns, 1982-1983, Spring, Grades 9-10 Question 1

• Enlarging a Rectangle

  A rectangle is given in the plane. Is it possible that after each side of the rectangle is increased by 1 cm, the area increases by 1 square meter? Provide an example or prove that it is impossible.

  (If the rectangle is 1x5, it becomes 2x6 and no side can be 0)

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  Topics:

  Geometry -> Area Calculation Algebra -> Equations Algebra -> Word Problems
  Sources:
  • Grossman Math Olympiad, 2017, Juniors Question 1

• How a Wheel Turns

  All 6 wheels in the diagram rotate as they touch each other without slipping. The diameter of the leftmost wheel is 15.7 cm and it makes 12 revolutions per minute.

  It is known that the smallest wheel makes one revolution per second.

  What is the diameter of the smallest wheel?

  

  Topics:

  Arithmetic Geometry -> Plane Geometry -> Circles Algebra -> Word Problems
  Sources:
  • Bar-Ilan's weekly mathriddle competition, 2024 Question 7

• Question

  Eighth-grade students threw rubber balls into a box and then tried to guess how many balls had accumulated there. Five students tried to guess: 45, 41, 55, 50, 43, but no one guessed the exact amount. The guesses differed from the truth by 3, 7, 5, 7, and 2 balls (not necessarily in the same order as the guesses). How many balls were in the box?

  Topics:

  Number Theory Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Beno Arbel Olympiad, 2017, Grade 8 Question 1

• Question

  Given several heavy boxes that can be transported using 7 trucks with a capacity of 6 tons each, but cannot be transported using 6 trucks of the same type.
  a. Is it possible to transport them with 3 trucks with a capacity of 7 tons each?
  b. Is it possible to transport them with 3 trucks with a capacity of 10 tons each?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Minimum and Maximum Problems / Optimization Problems
  Sources:
  • Beno Arbel Olympiad, 2017, Grade 8 Question 5