Take X to be the price of one barrel. For the 59 that crossed the border, Anatole paid 5 barrels plus 40 dollars. Thus, he paid 5X + 40.
This was the tax due for the 59 barrels; to find out the value of the tax paid for one barrel we need to divide it by 59. So the tax paid by Anatole per barrel was
(5X+40)/59
For the 18 barrels that she crossed the border with, Carla paid 2 barrels and received 40 dollars in return. Thus, Carla paid 2X-40 for the 18 barrels.
This way, the tax paid by Carla per barrel was
(2X-40)/18
Since both fractions represent the value paid for one barrel, they must be equal. Thus, we have:
(5X+40)/59 = (2X-40)/18
∴ 90X + 720 = 118X – 2,360 =>28X = 3,080 => X = 110
Thus, 110 dollars is the price of one barrel.
The total amount paid in tax for the 77 barrels was 7 barrels. Thus, the total amount of tax charged was 770 dollars. We know that 77 barrels crossed the border. Thus, each barrel had
770 / 77
of tax on them, that is, each barrel was taxed 10 dollars.
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