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A mathematician goes into a supermarket and buys three items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £5.88" and the checkout attendant, correctly adding the items, agrees.

Can you find the values of the three items?

Once you've had a chance to think about the problem, you may like to look at Getting Started, where you can watch some video clips of Alison working on the problem. 

I wonder if the same can happen with other values?
Alison wrote a computer program, and found three values that add together and multiply together to give £5.49.
Can you find them?

Alison's program also found three values that add together and multiply together to give £5.55. Can you find these?

You may wish to write a program of your own - if you do, we would love to hear about it. Remember, if you send us a solution to any of these problems, be sure to explain your thinking!


Extension
 

A mathematician goes into a supermarket and buys four items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £7.11" and the checkout attendent, correctly adding the items, agrees.

Find four possible prices of the items.


Very Challenging Extension: Prove that the costs giving rise to £7.11 are unique.
 
This problem is adapted from "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education