Problem: Matty has a basket of apples. If he were to double the quantity of apples he currently has while giving away its fifth, he would be left with 18. How many apples would he have to begin with?
Modern method: let x be
the number of apples.
Egyptian ‘false
position’: Try x = 5.
So, we get f(5) = 9 when x = 5. We want f(x) = 18, but notice that f(5) = 9, which is half of f(x) = 18. We can try x=10:
We can conclude that x
= 10 gives us the same solution using the modern method.
Therefore, we can conclude that Matty would have had 10 apples to begin with.
Nicely done! I like the comparison of a modern algebraic solution with the solution by false position.
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