A donkey and a mule were carrying bags of corn. If the mule gave the donkey 1 bag, they would have the same number. if the donkey gave the mule 1 bag, the mule would have twice as many bags as the donkey. how many bags is each carryung?
mule has 7 and donkey has 5
mule has 7 and donkey has five
Let's assume that the donkey is carrying x bags and the mule is carrying y bags.
According to the given information:
1. If the mule gave the donkey 1 bag, then the donkey would have x + 1 bags and the mule would have y - 1 bags.
2. In this case, the number of bags would be the same, so we can set up the equation: x + 1 = y - 1.
3. If the donkey gave the mule 1 bag, then the donkey would have x - 1 bags and the mule would have y + 1 bags.
4. In this case, the mule would have twice as many bags as the donkey, so we can set up the equation: y + 1 = 2(x - 1).
Let's solve the equations to find the values of x and y:
From equation 1: x + 1 = y - 1
Arranging terms: x - y = -2 (Equation 1)
From equation 2: y + 1 = 2(x - 1)
Expanding and rearranging terms: y + 1 = 2x - 2
Simplifying: 2x - y = 3 (Equation 2)
Now we have a system of equations:
x - y = -2 (Equation 1)
2x - y = 3 (Equation 2)
To solve this system, we can use either substitution or elimination method. Let's use the elimination method to solve this particular system:
Multiply Equation 1 by 2:
2x - 2y = -4 (Equation 3)
Next, subtract Equation 3 from Equation 2:
(2x - y) - (2x - 2y) = 3 - (-4)
Simplifying: y = 3 + 4
y = 7
Now substitute the value of y into Equation 1:
x - 7 = -2
Adding 7 to both sides: x = 5
Therefore, the donkey is carrying 5 bags, and the mule is carrying 7 bags.