text: # Resources tagged with: Simultaneous equations
  
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  ### There are 39 results
  
  Broad Topics > Algebraic expressions, equations and formulae > Simultaneous equations
  
  ### Multiplication Arithmagons
  
  ##### Age 14 to 16 Challenge Level:
  
  Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
  
  ### Arithmagons
  
  ##### Age 11 to 16 Challenge Level:
  
  Can you find the values at the vertices when you know the values on the edges?
  
  ### Colour Islands Sudoku
  
  ##### Age 11 to 14 Challenge Level:
  
  An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
  
  ### Quadruple Clue Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
  
  ### Intersection Sudoku 1
  
  ##### Age 11 to 16 Challenge Level:
  
  A Sudoku with a twist.
  
  ### Simultaneous Equations Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  Solve the equations to identify the clue numbers in this Sudoku problem.
  
  ### Addition Equation Sudoku
  
  ##### Age 11 to 14 Challenge Level:
  
  You need to find the values of the stars before you can apply normal Sudoku rules.
  
  ### Another Quadruple Clue Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
  
  ### Intersection Sudoku 2
  
  ##### Age 11 to 16 Challenge Level:
  
  A Sudoku with a twist.
  
  ### Gift of Gems
  
  ##### Age 14 to 16 Challenge Level:
  
  Four jewellers share their stock. Can you work out the relative values of their gems?
  
  ### Building Tetrahedra
  
  ##### Age 14 to 16 Challenge Level:
  
  Can you make a tetrahedron whose faces all have the same perimeter?
  
  ### Children at Large
  
  ##### Age 11 to 14 Challenge Level:
  
  There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
  
  ### Matchless
  
  ##### Age 14 to 16 Challenge Level:
  
  There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
  
  ### All-variables Sudoku
  
  ##### Age 11 to 18 Challenge Level:
  
  The challenge is to find the values of the variables if you are to solve this Sudoku.
  
  ### Overturning Fracsum
  
  ##### Age 14 to 16 Challenge Level:
  
  Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
  
  ### Negatively Triangular
  
  ##### Age 14 to 16 Challenge Level:
  
  How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
  
  ### Pareq Calc
  
  ##### Age 14 to 16 Challenge Level:
  
  Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
  
  ### LCM Sudoku II
  
  ##### Age 11 to 18 Challenge Level:
  
  You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
  
  ### Which Is Bigger?
  
  ##### Age 14 to 16 Challenge Level:
  
  Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
  
  ### Which Is Cheaper?
  
  ##### Age 14 to 16 Challenge Level:
  
  When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
  
  ### The Simple Life
  
  ##### Age 11 to 14 Challenge Level:
  
  The answer is $5x+8y$... What was the question?
  
  ### Warmsnug Double Glazing
  
  ##### Age 14 to 16 Challenge Level:
  
  How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
  
  ### Polycircles
  
  ##### Age 14 to 16 Challenge Level:
  
  Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
  
  ### Sweet Shop
  
  ##### Age 11 to 14 Challenge Level:
  
  Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.
  
  ### Not a Polite Question
  
  ##### Age 11 to 14 Short Challenge Level:
  
  When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
  
  ### Letter Land
  
  ##### Age 11 to 14 Challenge Level:
  
  If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
  
  ### CD Heaven
  
  ##### Age 14 to 16 Challenge Level:
  
  All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .
  
  ### All Square
  
  ##### Age 11 to 14 Challenge Level:
  
  Solve the system of equations xy = 1 yz = 4 zx = 9
  
  ### Symmetricality
  
  ##### Age 11 to 14 Challenge Level:
  
  Add up all 5 equations given below. What do you notice? Solve the system and find the values of a, b, c , d and e. b + c + d + e = 4 a + c + d + e = 5 a + b + d + e = 1 a + b + c + e = 2 a + b. . . .
  
  ### Surds
  
  ##### Age 14 to 16 Challenge Level:
  
  Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
  
  ### Leonardo's Problem
  
  ##### Age 14 to 18 Challenge Level:
  
  A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
  
  ### A Method of Defining Coefficients in the Equations of Chemical Reactions
  
  ##### Age 14 to 18
  
  A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
  
  ### Rudolff's Problem
  
  ##### Age 14 to 16 Challenge Level:
  
  A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
  
  ### Coffee
  
  ##### Age 14 to 16 Challenge Level:
  
  To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
  
  ### Intersections
  
  ##### Age 14 to 18 Challenge Level:
  
  Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
  
  ### What's it Worth?
  
  ##### Age 11 to 16 Challenge Level:
  
  There are lots of different methods to find out what the shapes are worth - how many can you find?
  
  ### Fruity Totals
  
  ##### Age 7 to 16 Challenge Level:
  
  In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
  
  ### Whole Numbers Only
  
  ##### Age 11 to 14 Short Challenge Level:
  
  Can you work out how many of each kind of pencil this student bought?
  
  ### Always Two
  
  ##### Age 14 to 18 Challenge Level:
  
  Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
explanation: This document is a collection of problems and challenges related to simultaneous equations, presented in a format typical of educational resources. Each problem is designed to test the reader's ability to solve systems of equations, often in the context of puzzles or real-world scenarios. The document does not contain a single question and answer but rather multiple problems that require the reader to find solutions.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Resources tagged with: Simultaneous equations
  
  Filter by: Content type:
  Age range:
  Challenge level:
  
  ### There are 39 results
  
  Broad Topics > Algebraic expressions, equations and formulae > Simultaneous equations
  
  ### Multiplication Arithmagons
  
  ##### Age 14 to 16 Challenge Level:
  
  Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
  
  ### Arithmagons
  
  ##### Age 11 to 16 Challenge Level:
  
  Can you find the values at the vertices when you know the values on the edges?
  
  ### Colour Islands Sudoku
  
  ##### Age 11 to 14 Challenge Level:
  
  An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
  
  ### Quadruple Clue Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
  
  ### Intersection Sudoku 1
  
  ##### Age 11 to 16 Challenge Level:
  
  A Sudoku with a twist.
  
  ### Simultaneous Equations Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  Solve the equations to identify the clue numbers in this Sudoku problem.
  
  ### Addition Equation Sudoku
  
  ##### Age 11 to 14 Challenge Level:
  
  You need to find the values of the stars before you can apply normal Sudoku rules.
  
  ### Another Quadruple Clue Sudoku
  
  ##### Age 11 to 16 Challenge Level:
  
  This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
  
  ### Intersection Sudoku 2
  
  ##### Age 11 to 16 Challenge Level:
  
  A Sudoku with a twist.
  
  ### Gift of Gems
  
  ##### Age 14 to 16 Challenge Level:
  
  Four jewellers share their stock. Can you work out the relative values of their gems?
  
  ### Building Tetrahedra
  
  ##### Age 14 to 16 Challenge Level:
  
  Can you make a tetrahedron whose faces all have the same perimeter?
  
  ### Children at Large
  
  ##### Age 11 to 14 Challenge Level:
  
  There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
  
  ### Matchless
  
  ##### Age 14 to 16 Challenge Level:
  
  There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
  
  ### All-variables Sudoku
  
  ##### Age 11 to 18 Challenge Level:
  
  The challenge is to find the values of the variables if you are to solve this Sudoku.
  
  ### Overturning Fracsum
  
  ##### Age 14 to 16 Challenge Level:
  
  Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
  
  ### Negatively Triangular
  
  ##### Age 14 to 16 Challenge Level:
  
  How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
  
  ### Pareq Calc
  
  ##### Age 14 to 16 Challenge Level:
  
  Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
  
  ### LCM Sudoku II
  
  ##### Age 11 to 18 Challenge Level:
  
  You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
  
  ### Which Is Bigger?
  
  ##### Age 14 to 16 Challenge Level:
  
  Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
  
  ### Which Is Cheaper?
  
  ##### Age 14 to 16 Challenge Level:
  
  When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
  
  ### The Simple Life
  
  ##### Age 11 to 14 Challenge Level:
  
  The answer is $5x+8y$... What was the question?
  
  ### Warmsnug Double Glazing
  
  ##### Age 14 to 16 Challenge Level:
  
  How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
  
  ### Polycircles
  
  ##### Age 14 to 16 Challenge Level:
  
  Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
  
  ### Sweet Shop
  
  ##### Age 11 to 14 Challenge Level:
  
  Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.
  
  ### Not a Polite Question
  
  ##### Age 11 to 14 Short Challenge Level:
  
  When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
  
  ### Letter Land
  
  ##### Age 11 to 14 Challenge Level:
  
  If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
  
  ### CD Heaven
  
  ##### Age 14 to 16 Challenge Level:
  
  All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .
  
  ### All Square
  
  ##### Age 11 to 14 Challenge Level:
  
  Solve the system of equations xy = 1 yz = 4 zx = 9
  
  ### Symmetricality
  
  ##### Age 11 to 14 Challenge Level:
  
  Add up all 5 equations given below. What do you notice? Solve the system and find the values of a, b, c , d and e. b + c + d + e = 4 a + c + d + e = 5 a + b + d + e = 1 a + b + c + e = 2 a + b. . . .
  
  ### Surds
  
  ##### Age 14 to 16 Challenge Level:
  
  Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
  
  ### Leonardo's Problem
  
  ##### Age 14 to 18 Challenge Level:
  
  A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
  
  ### A Method of Defining Coefficients in the Equations of Chemical Reactions
  
  ##### Age 14 to 18
  
  A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
  
  ### Rudolff's Problem
  
  ##### Age 14 to 16 Challenge Level:
  
  A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
  
  ### Coffee
  
  ##### Age 14 to 16 Challenge Level:
  
  To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
  
  ### Intersections
  
  ##### Age 14 to 18 Challenge Level:
  
  Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
  
  ### What's it Worth?
  
  ##### Age 11 to 16 Challenge Level:
  
  There are lots of different methods to find out what the shapes are worth - how many can you find?
  
  ### Fruity Totals
  
  ##### Age 7 to 16 Challenge Level:
  
  In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
  
  ### Whole Numbers Only
  
  ##### Age 11 to 14 Short Challenge Level:
  
  Can you work out how many of each kind of pencil this student bought?
  
  ### Always Two
  
  ##### Age 14 to 18 Challenge Level:
  
  Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: This document is a collection of problems and challenges related to simultaneous equations, presented in a format typical of educational resources. Each problem is designed to test the reader's ability to solve systems of equations, often in the context of puzzles or real-world scenarios. The document does not contain a single question and answer but rather multiple problems that require the reader to find solutions.
  
  Label: multiple-question