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There are **50** NRICH Mathematical resources connected to **Simultaneous equations**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### Fruity Totals

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Arithmagons

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Is Bigger?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Is Cheaper?

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Negatively Triangular

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matchless

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 ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Intersections

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Warmsnug Double Glazing

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arithmagons

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Children at Large

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sweet Shop

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Leonardo's Problem

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Letter Land

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### CD Heaven

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 each price?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Surds

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### System Speak

Five equations... five unknowns... can you solve the system?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Always Two

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadratic Harmony

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Graphs of Changing Areas

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cobalt Decay

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LCM Sudoku II

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Addition Equation Sudoku

You need to find the values of the stars before you can apply normal Sudoku rules.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Another Quadruple Clue Sudoku

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Colour Islands Sudoku

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadruple Clue Sudoku

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### All-variables Sudoku

The challenge is to find the values of the variables if you are to solve this Sudoku.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Simultaneous Equations Sudoku

Solve the equations to identify the clue numbers in this Sudoku problem.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walls

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Many Balls?

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### A Method of Defining Coefficients in the Equations of Chemical Reactions

A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Pareq Calc

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 lines are 1 unit and 2 units.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Symmetricality

Five equations and five unknowns. Is there an easy way to find the unknown values?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Whole Numbers Only

Can you work out how many of each kind of pencil this student bought?

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Not a Polite Question

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...

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Coffee

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Escriptions

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pair Squares

The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polycircles

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rudolff's Problem

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Overturning Fracsum

Can you solve the system of equations to find the values of x, y and z?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Age 16 to 18

Challenge Level