Resources tagged with Simultaneous equations similar to Sums of Pairs:
Other tags that relate to Sums of Pairs
Inequality/inequalities. Trial and improvement. Manipulating algebraic expressions/formulae. Making and proving conjectures. Creating expressions/formulae. Polynomials. Mathematical reasoning & proof. Factorisation (algebraic). Graphs. Generalising.There are 36 results
Broad Topics > Algebra > Simultaneous equations
Leonardo's Problem
Stage: 4 and 5 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?
Matchless
Stage: 4 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 ?
Gift of Gems
Stage: 4 Challenge Level:
Four jewellers share their stock. Can you work out the relative values of their gems?
Always Two
Stage: 4 and 5 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.
All-variables Sudoku
Stage: 3, 4 and 5 Challenge Level:
The challenge is to find the values of the variables if you are to solve this Sudoku.
Overturning Fracsum
Stage: 4 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
Polycircles
Stage: 4 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?
Multiplication Arithmagons
Stage: 4 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Arithmagons
Stage: 4 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
Children at Large
Stage: 3 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?
Which Is Cheaper?
Stage: 4 Challenge Level:
When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?
Coffee
Stage: 4 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?
Which Is Bigger?
Stage: 4 Challenge Level:
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Pareq Calc
Stage: 4 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. . . .
Rudolff's Problem
Stage: 4 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?
Intersections
Stage: 4 and 5 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?
Stage: 3 and 4 Challenge Level:
There are lots of different methods to find out what the shapes are worth - how many can you find?
Surds
Stage: 4 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
CD Heaven
Stage: 4 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. . . .
Quadruple Clue Sudoku
Stage: 3 and 4 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.
LCM Sudoku II
Stage: 3, 4 and 5 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Building Tetrahedra
Stage: 4 Challenge Level:
Can you make a tetrahedron whose faces all have the same perimeter?
Symmetricality
Stage: 3 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. . . .
Another Quadruple Clue Sudoku
Stage: 3 and 4 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.
Simultaneous Equations Sudoku
Stage: 3 and 4 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
Negatively Triangular
Stage: 4 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 ?
Letter Land
Stage: 3 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.
Sweet Shop
Stage: 3 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.
Whole Numbers Only
Stage: 3 Challenge Level:
Can you work out how many of each kind of pencil this student bought?
Not a Polite Question
Stage: 3 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...
A Method of Defining Coefficients in the Equations of Chemical Reactions
Stage: 4 and 5
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
Colour Islands Sudoku
Stage: 3 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.
Addition Equation Sudoku
Stage: 3 Challenge Level:
You need to find the values of the stars before you can apply normal Sudoku rules.
NRICH is part of the family of activities in the Millennium Mathematics Project.