Let's assume that a donkey is carrying "x" bales and a horse is carrying "y" bales.
(1.) If a horse will give to a donkey 1 bale, then a horse will be carrying (y  1) bales and a donkey will be carrying (x + 1) bales, which will be half as much as horse's.
So, we can write first equation:
1
x + 1 = (y  1)
2
(2.) From other side, if a donkey will give 1 bale to a horse, then a donkey will be carrying (x  1) bales and a horse will be carrying (y + 1) bales, which is 3 times as much as donkey's.
Thereby, we can write second equation:
y + 1 = 3(x  1)
Now, let's solve system of two equations:
x + 1 = 0.5(y  1)
y + 1 = 3(x  1)
Let's open parentheses and move all variables on the left side of each equation and numbers on the right side:
x + 1 = 0.5y  0.5
y + 1 = 3x  3
x  0.5y =  1  0.5
3x + y =  1  3
2x  y = 3
+
 3x + y =  4

 x =  7
x = 7
Let's plug in the value of "x" into second original equation
y + 1 = 3(7  1)
y = 18  1 = 17
Originally, a donkey was carrying 7 bales and a horse was carrying 17 bales.
12/1/2013

Nataliya D.