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.

• Question

  Three hedgehogs have three pieces of cheese weighing `5`, `8`, and `11` grams. A fox offers to help the hedgehogs divide the cheese equally. The fox can bite off one gram from each of two cheese pieces of its choice. Can the fox, using these actions, reach a state where it leaves the three hedgehogs with equal pieces of cheese?

  Topics:

  Arithmetic Algebra -> Word Problems Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division
  Sources:
  • problems.ru web site

• The broken chain

  There are five segments of a broken chain, each segment having three links. Moses wants to repair the chain. What is the minimum number of links he needs to open and close again to join all these segments together?

  Note: The chain is not circular!

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Proof and Example -> Constructing an Example / Counterexample Minimum and Maximum Problems / Optimization Problems

• Question

  There are two coins in a wallet, and their sum is `15` shekels. One of the coins is not a `5` shekel coin. What are the coins in the wallet?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  One-seventh of mathematicians are philosophers, and one-ninth of philosophers are mathematicians. Which are there more of – philosophers or mathematicians?

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  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Arithmetic -> Fractions
  Sources:
  • problems.ru web site

• Question

  A cube with a side length of one meter is cut into cubes with a side length of one centimeter. If all the resulting cubes are placed in a row, what will be the length of the row?

  Topics:

  Geometry -> Solid Geometry / Geometry in Space Arithmetic Algebra -> Word Problems Units of Measurement

• Question

  Shuki walked for 3.5 hours. In each hour-long period, he traveled 5 km. Does it follow that Shuki's average speed during this entire time was 5 km per hour?

  Topics:

  Algebra -> Word Problems Algebra -> Inequalities -> Averages / Means

• Question

  How can you divide `7` apples equally among `12` children, if you are not allowed to cut any apple into more than `5` pieces?

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  Topics:

  Algebra -> Word Problems Arithmetic -> Fractions Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division
  Sources:
  • problems.ru web site

• Movie Buffs

  Avi, Beni, and Gili love movies. Avi goes to the movies every `3` days, Beni – every `5` days, and Gili goes every `7` days. Today, they all went to the movies together. In how many days can this happen again?

  Topics:

  Arithmetic Algebra -> Word Problems Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
  Sources:
  • problems.ru web site

• Question

  The "Sweet Math" candies are sold in boxes of `12` units, and the "Geometry with Nuts" candies – in boxes of `15` units.

  What is the minimum number of boxes that must be purchased so that there are equal quantities of candies of both types?

  Topics:

  Arithmetic Algebra -> Word Problems Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Minimum and Maximum Problems / Optimization Problems
  Sources:
  • problems.ru web site

• Question

  Shmuel's salary increased by `20%`, and then decreased by `20%`. Is Shmuel's current salary equal to his initial salary?

  Topics:

  Algebra -> Word Problems Arithmetic -> Percentages
  Sources:
  • problems.ru web site