Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20. Since they have not enough money to pay the custom duties, the first pays 5 casks of wine and 40 francs, and the second pays 2 casks of wine and receives 40 francs in change. What is the price of each cask of wine and the duty on it?
LEt P be the Price of each cast of wine, and D be the percent duty.
64P*D=5P+40
20P*D=2P-40
multiply the second equation by 3.2
64PD=5P+40
64PD=6.4P-128
subtract the second from the first.
0=-1.4P+168
solve for P
then, go back to the original equation (either) and solve for D
To solve this problem, we need to set up a system of equations based on the given information. Let's denote the price of each cask of wine as 'x' and the duty on each cask of wine as 'y'.
From the first part of the information, we know that one wine merchant pays 5 casks of wine and 40 francs, so we can write the equation:
5x + 40 = total cost for the first merchant
From the second part of the information, we know that the other wine merchant pays 2 casks of wine and receives 40 francs in change, so we can write the equation:
2x - 40 = total cost for the second merchant
We also know that the total number of casks of wine brought by both merchants is 64 + 20 = 84, so we can write another equation:
5 casks + 2 casks = 84
Combining these equations, we can solve for the price of each cask (x) and the duty on each cask (y):
5x + 40 = 84
2x - 40 = 40
5x + 2x = 84 - 40
Simplifying the equations, we get:
7x + 40 = 84
2x - 40 = 40
7x = 44
Solving for x, we find:
x = 44 / 7
x = 6.29
Therefore, the price of each cask of wine is approximately 6.29 francs.
Now, to find the duty on each cask (y), we substitute the value of x back into one of the equations:
2(6.29) - 40 = y
12.58 - 40 = y
-27.42 = y
Therefore, the duty on each cask of wine is approximately 27.42 francs.