Pay for an employee work for a month (that is, thirty days) is 10 dinars and a dress. The employee worked three days only and earned the dress only. What is the price of the dress?(Source: this terribly formatted PDF on arXiv)
Answer given in source but no justification given. What is the answer and why? Let's represent the month's salary as $10 + x$, where $x$ is the price of the dress in dinars. Let's assume that working for exactly one-tenth of the month means getting exactly one-tenth of the pay. Then the value of wages paid in cash and in kind is $\frac{10 + x}{10}$. This value is equal to the price of the dress, so $\frac{10 + x}{10} = x$, therefore $1 + \frac{x}{10} = x$ and then $1 = \frac{9}{10}x$. Accordingly, $x = \frac{10}{9}$, just a little over one dinar.
(The most valuable dinar at the time of this posting is the Kuwaiti dinar, currently worth 3.32 USD each. Admittedly naively comparing this medieval dinar to any modern one and not correcting for inflation, the monthly wages for this worker would then be under 37 USD. Those were the days, when money really had value!)
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