Diophantus of Alexandria/Arithmetica/Book 1/Problem 8

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Problem

What number must be added to $100$ and to $20$ (the same number added to each) so that the sums are in the ratio $3 : 1$?


Solution

$20$


Proof

Let $x$ be the number added.

Then we have:

\(\ds 100 + x\) \(=\) \(\ds 3 \paren {20 + x}\)
\(\ds \leadsto \ \ \) \(\ds 100 - 60\) \(=\) \(\ds 2 x\) rearranging
\(\ds \leadsto \ \ \) \(\ds x\) \(=\) \(\ds 20\) simplifying

$\blacksquare$


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