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.

• Parentheses

  Add parentheses to make the result as large as possible:

  `10000-1000-100-10-1`

  Topics:

  Arithmetic Algebra -> Equations Minimum and Maximum Problems / Optimization Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 2
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 5-6 Question 1

• Sum of Squares

  Given a rectangle with an area of 13 and a perimeter of 20. On two adjacent sides of the rectangle, two squares are constructed, as shown in the figure. Find the sum of the areas of the squares.

  

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  Topics:

  Geometry -> Area Calculation Algebra -> Equations Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 7

• Sun Minus Five

  In the following arithmetic problems, different letters replace different digits, and identical letters replace
  identical digits.
  `5 = ש + מ + ח`
  `9 = ש + מ + ש`
  Calculate the value of the expression: `ח + ש`

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 2

• How Much is Happy?

  In the following arithmetic exercises, different letters replace different digits, and identical letters replace identical digits.
  `19 = ט + מ + ח + ש`
  `10 = ק + ח + ש + מ`
  Calculate the value of the expression: `ח + מ + ש`

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 2

• The Bakery

  In the morning, a bakery's storage room contained 135 kilograms of flour and 92 kilograms of sugar.
  To bake one cake, the baker uses one kilogram of flour and one kilogram of sugar.
  At the end of the workday, the amount of flour remaining for the baker was twice as large as the amount of sugar remaining.
  How many cakes did the baker make during the workday?

  Topics:

  Algebra -> Equations Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 3-4 Question 5
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 2

• SLV LVS BLS

  In the following expression, different letters represent different digits, and identical letters represent identical digits:

  SLV = LVS + BLS

  Find the number SLV.

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rule by 11 Algebra -> Equations Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 3

• Question

  In the following addition problem, different shapes replace different digits, and identical shapes replace identical digits:

  `triangle square triangle square triangle+ square triangle square triangle square = o+ triangle triangle triangle triangle o+`

  What is the result of the addition?

  Topics:

  Arithmetic Algebra -> Equations Logic -> Reasoning / Logic Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 3

• Average of Averages

  Consider the following diagram:

  

  Each number in the diagram, connected to 4 other numbers, must be equal to their average:
  What is the number in the circle marked with a question mark?
  Note: The average of four numbers is their sum divided by 4.

  Topics:

  Algebra -> Equations Algebra -> Inequalities -> Averages / Means
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 1

• Average of Averages 2

  Consider the following diagram:

  

  Each number in the diagram, connected to 4 other numbers, must be equal to their average:
  What is the number in the circle marked with a question mark?

  Topics:

  Algebra -> Equations Algebra -> Inequalities -> Averages / Means
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 1

• Length of the Segment

  On the side BC of triangle ABC, a point D is marked. The perimeter of triangle ABC is 15 centimeters, the perimeter of triangle ABD is 12 centimeters, and the perimeter of triangle ACD is 13 centimeters.
  What is the length of segment AD?

  Topics:

  Geometry -> Plane Geometry -> Triangles Algebra -> Equations
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 2