Algebra, Equations

An equation is a statement that two mathematical expressions are equal. Solving an equation involves finding the values of variables that make the statement true. Questions cover various types: linear, quadratic, polynomial, rational, radical, and systems of equations.

• Question

  Insert arithmetic operation symbols and parentheses so that the equality becomes correct:

  5    5    5  = 0

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses

• Hanukkah Money

  Two brothers, Yosef and Danny, received Hanukkah money. Afterward, Danny said to Yosef: "If you give me `8` shekels, then I will have twice as much money as you." Yosef replies: "I think that's not very fair. I think it's better if you give me `8` shekels, and then we will have the same amount of money." How much Hanukkah money did each brother receive?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  Danny and Rachel are brother and sister. The number of Danny's brothers equals the number of his sisters. The number of Rachel's brothers is twice as large as the number of her sisters. How many boys and how many girls are there in this family?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  Two workers pave two kilometers of road within two days. How many workers are needed to pave `20` kilometers of road within `20` days?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division

• Question

  There are `29` students in a class. The number of boys is `3` more than the number of girls. How many boys and how many girls are there in the class?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  In Danny's class there are `30` students. Danny claims that the number of boys is greater by `3` than the number of girls. Is it possible that Danny is right?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd)

• 5 = 6?

  Here is a "proof" that `5` is equal to `6`:

  `35+10-41=42+12-50 `

  `35+10-45=42+12-54 `

  `5*(7+2-9)=6*(7+2-9) `

  ׂ`5=6`

  Where is the mistake?

  Topics:

  Arithmetic Algebra -> Equations Number Theory -> Division

• Question

  It is known that `a = b+1`. Is it possible that `a^4=b^4`?

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  Topics:

  Arithmetic Algebra -> Equations
  Sources:
  • problems.ru web site

• Question

  I went to the market to buy vegetables. I paid for tomatoes half of the money I had plus one shekel. After that, I paid for cucumbers half of the remaining money plus one shekel, and then I paid for onions half of the remaining money plus one shekel, and that used up all the money I had.

  What is the amount of money I came to the market with?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems -> Solving Word Problems "From the End" / Working Backwards
  Sources:
  • problems.ru web site

• The Sophisticated Task

  Hannah has a basket with `13` apples. Hannah wants to know the total weight of all these apples. Rachel has a digital scale, and she is willing to help Hannah, but only under the following conditions: In each weighing, Hannah can weigh exactly `2` apples, and the number of weighings cannot exceed `8`.

  Explain how, under these conditions, Hannah can know the total weight of the apples.

  Topics:

  Combinatorics -> Double Counting Algebra -> Equations Algebra -> Word Problems Proof and Example -> Constructing an Example / Counterexample Algorithm Theory -> Weighing
  Sources:
  • problems.ru web site