done by bobpursely about 2 weeks ago ...
http://www.jiskha.com/display.cgi?id=1282663289
http://www.jiskha.com/display.cgi?id=1282663289
Donkey; 2
According to the given information, if the donkey gave one sack to the mule, then the mule would have twice as many sacks as the donkey. This can be represented by the equation:
y + 1 = 2(x - 1)
Also, if the mule gave one sack to the donkey, then both would have equal loads. This can be represented by the equation:
x + 1 = y - 1
Now, let's solve these two equations to find the values of x and y.
Equation 1: y + 1 = 2(x - 1)
Expanding the equation:
y + 1 = 2x - 2
Moving all terms to one side:
2x - y = 3 ---- (Equation 1)
Equation 2: x + 1 = y - 1
Moving terms to one side:
x - y = -2 ---- (Equation 2)
Now, we can solve these two equations simultaneously.
Multiplying Equation 2 by 2:
2x - 2y = -4 ---- (Equation 3)
Equation 1 minus Equation 3:
2x - y - (2x - 2y) = 3 - (-4)
2x - y - 2x + 2y = 3 + 4
-x + 3y = 7 ---- (Equation 4)
Simplifying Equation 4:
x = 3y - 7
Substituting this value of x into Equation 2:
3y - 7 - y = -2
2y = 5
y = 5/2
y = 2.5
Substituting this value of y into Equation 2:
x - 2.5 = -2
x = -2 + 2.5
x = 0.5
So, the donkey was carrying 0.5 sacks of apples, and the mule was carrying 2.5 sacks of apples.
According to the information given, the mule says that if the donkey gave it one sack, then the mule would have twice as many as the donkey. In equation form, this can be written as:
M + 1 = 2(D - 1)
Similarly, the mule also says that if it gave the donkey one of its sacks, then they would have equal loads. In equation form, this can be written as:
M - 1 = D + 1
Now, we have a system of two equations with two variables. We can solve this system to find the values of D and M.
Let's start by solving the first equation:
M + 1 = 2(D - 1)
Expanding and simplifying:
M + 1 = 2D - 2
M = 2D - 3
Now, let's substitute this expression for M into the second equation:
(2D - 3) - 1 = D + 1
2D - 4 = D + 1
Subtracting D from both sides:
D - 4 = 1
Adding 4 to both sides:
D = 5
Now, substitute this value of D back into either of the equations to find the value of M:
M = 2(5) - 3
M = 7
Therefore, the donkey is carrying 5 sacks, and the mule is carrying 7 sacks.