Answer:
So, the farmer had 220 more sheep than goats in the beginning.
Explanation:
To find the number of goats and sheep the farmer had in the beginning, we can start by assigning variables. Let's say the number of goats is "g" and the number of sheep is "s".
According to the problem, the farmer sold 3/4 of his goats, which means he kept 1/4 of his goats. This can be represented as (1/4)g. Additionally, the farmer sold 400 sheep, so the number of sheep left is s - 400.
We are given that if the farmer sold 3/4 of his goats and 400 sheep, he would have an equal number of goats and sheep left. This can be expressed as:
(1/4)g = s - 400
To solve this equation, we need to find the relationship between g and s. Since we are interested in finding the difference between the number of sheep and goats, we can rearrange the equation to solve for g:
(1/4)g = s - 400
g = 4(s - 400)
Next, we substitute the value of g in terms of s into the total number of goats and sheep:
g + s = 700
4(s - 400) + s = 700
Now, we can solve for s:
4s - 1600 + s = 700
5s - 1600 = 700
5s = 2300
s = 460
Finally, we can find the number of goats in the beginning:
g = 4(s - 400)
g = 4(460 - 400)
g = 240
Therefore, the farmer had 240 goats and 460 sheep in the beginning. To find the difference, we subtract the number of goats from the number of sheep:
460 - 240 = 220
So, the farmer had 220 more sheep than goats in the beginning.