word problems and turning them into algebraic equation to slove

A donkey and a horse were carrying some bales of cloth. the donkey said to the horse "if you give me one of your bales of cloth, I shall carry half as much as you". The horse replied " If you give me one of yours, I will be carrying three times as much as you". How many bales was each animal carrying originally?( to start with)

Use variables, set up as an equation for solving.....

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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.