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Resources tagged with Simultaneous equations similar to Gift of Gems:

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Broad Topics > Algebra > Simultaneous equations

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Gift of Gems

Stage: 4 Challenge Level: Challenge Level:1

Four jewellers possessing respectively eight rubies, ten saphires, a hundred pearls and five diamonds, presented, each from his own stock, one apiece to the rest in token of regard; and they. . . .

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Leonardo's Problem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Pareq Calc

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Multiplication Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

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

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Pentagon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the vertices of a pentagon given the midpoints of its sides.

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Polycircles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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System Speak

Stage: 4 and 5 Challenge Level: Challenge Level:1

Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?

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All-variables Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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Children at Large

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Always Two

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Surds

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Bang's Theorem

Stage: 4 Challenge Level: Challenge Level:1

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

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Arithmagons

Stage: 3 Challenge Level: Challenge Level:1

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

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Intersection Sudoku 1

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

A Sudoku with a twist.

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Quadruple Clue Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.

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Equation Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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Another Quadruple Clue Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.

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Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

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Which Is Bigger?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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LCM Sudoku II

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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Addition Equation Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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Sweet Shop

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Symmetricality

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

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Negatively Triangular

Stage: 4 Challenge Level: Challenge Level:1

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

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Intersections

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

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Intersection Sudoku 2

Stage: 3 and 4 Challenge Level: Challenge Level:1

A Sudoku with a twist.

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What's it Worth?

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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CD Heaven

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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All Square

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Solve the system of equations xy = 1 yz = 4 zx = 9

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Coffee

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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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.

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Rudolff's Problem

Stage: 4 Challenge Level: Challenge Level:1

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?

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Overturning Fracsum

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Letter Land

Stage: 3 Challenge Level: Challenge Level:1

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.

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Not a Polite Question

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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...

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Whole Numbers Only

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Colour Islands Sudoku

Stage: 3 Challenge Level: Challenge Level:1

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