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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...

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Whole Numbers Only

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

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Symmetricality

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 + c + d = 0

Children at Large

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

Why do this problem?

This problem can be solved by either trial and improvement or, more formally, by making a set of two simultaneous equations. For this reason, it could be used as a method of introducing or revising simultaneous equations.

Key questions

How are you going to work on this? Are you going to use trial and improvement or try to make a set of simultaneous equations?
Would a number line for the children's ages help you?
Would it be useful to write the initial information as simultaneous equations?
Can you get two equations involving just two of the unknowns?
Whose ages are even and whose odd?
What combinations are possible for Tom's and Sally's ages?
Why not try a number or Tom's age and see how it works out?

Possible extension

Learners could go on to a similar problem such as Thasan's Dream.

Possible support

Suggest jotting down the useful information a number line for the children's ages.