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Solution: Let the total number of sheep be X, including sheep A and goat 84-A; Obviously, the total number of sheep remained the same before and after the sale.

Before sale: 7x/25 sheep and 18x/25 goat.

After sale: 63x/ 125 sheep, 62x/ 125 goat;

Get the equation:

7x/25-a+84 = 63x/ 125-( 1)

18x/25-(84-a)= 62x/ 125-(2)

(1)(2) The same equation is obtained after sorting.

x = 125* (84-a)/28

= 125*(3 - a/28)

Obviously, to make X a positive integer, A must be a multiple of 28, and 0 ≤ a/28 ≤2.

When a/28=0, that is, a=0, x=375:

Pre-sale: sheep =105; Goat = 270;

After sale: sheep =189; Goat =186;

The number of sheep is less than the original goat: 270- 189=8 1 (only)

When a/28= 1, that is, a=28 and x=250:

Before buying and selling: sheep = 70; Goat =180;

After sale: sheep =126; Goat =124;

The number of sheep is less than the original goat: 180- 126=54 (only)

When a/28=2, namely a=56, x= 125:

Before buying and selling: sheep = 35

Conclusion: The number of sheep is 8 1, that is, 54, which is less than the original goat.