Question

a mule and donkey were going to the market laden with wheat the mule said"if you give me one measure, i should carry twice as much as you, but if i give you one, we should have equal burdens."
what were there burdens?

Answer 1

The mule has m amount, and the donkey has d amount before they move the amounts around.
mule ---> m
donkey ---> d

If the donkey gives one measure, then the donkey will have d - 1 amount and the mule will have m + 1 amount.
Now they have:
mule ---> m + 1
donkey ---> d - 1

We are told this means the mule has twice the donkey's amount, so

m + 1 = 2(d - 1) Equation 1

Answer 2

We now have one equation is two variables.
We need a second equation, and we are given another piece of information that will let us find the second equation.

Answer 3

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Answer 4

If the mule gives one measure to the donkey, the burdens are equal.

mule ---> m - 1
donkey ---> d + 1

m - 1 = d + 1 Equation 2

Answer 5

Now we solve the two equations in a system of equations.
m + 1 = 2(d - 1) ---> m + 1 = 2d - 2 ---> m = 2d - 3
m - 1 = d + 1 m - 1 = d + 1 m = d + 2

Since both equations are solved for m, we set them equal to each other.

2d - 3 = d + 2
d = 5

m - 1 = d + 1
m - 1 = 5 + 1
m - 1 = 6
m = 7

The mule has 7 measures and the donkey has 5 measures.

Answer 6

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