Two wine merchants, Anatole and Carla, arrived at the border carrying barrels. Anatole carried 64 barrels and Carla carried 20 barrels. The 84 barrels were of equal weight.

Since they did not have enough money to pay the taxes for the crossing, they asked Marsha, the customs officer, whether they could use some of the barrels to pay the taxes they owed (each barrel had a value assigned by law).

Marsha was an understanding woman, so she agreed.

Because she was also very honest, example of employee, very righteous, she wanted to make sure that the correct tax was paid, so that the transaction would be perfectly legal.

After making some calculations (taking into account the price of each barrel and the value of the taxes), Marsha said:

- Anatole will pay 5 barrels plus 40 dollars. He will cross the border with 59 barrels. Carla will pay 2 barrels and will receive 40 dollars. She will cross the border with 18 barrels.

And so they did, both merchants agreeing with the calculations.

Anatole paid the 5 barrels plus 40 dollars and Carla paid 2 barrels and received 40 dollars.

They crossed the border with 59+18 barrels, that is, 77 barrels, and the taxes paid (for the 77 barrels) was 7 barrels because the Customs did not receive any part in money. The 40 dollars paid by Anatole were given to Carla.

We ask:

What was the price of each barrel? What was the tax paid over each barrel?

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Solution