[unlearner]

“There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”

Let S be the number of small dogs, and L be the number of large dogs:

Given:
S + L = 49
S - L = 36

Solution:
S - L = 36 becomes
S = L + 36
Substitute L + 36 for S in the first given so that
S + L = 49
becomes
(L + 36) + L = 49
simplify to
2L = 49 - 36 = 13
reduce both sides by dividing each by 2
2L/2 = 13/2
reduces to
L = 6.5
solving for S,
S + 6.5 = 49
S = 49 - 6.5 = 42.5

The number of small dogs would be 42.5.
And the number of large dogs wold be 6.5.

check your work...
42.5 + 6.5 = 49
42.5 - 6.5 = 36

It’s correct.

However, since we are dealing with dogs, the answer should be in whole numbers or the original proposal would be invalid. If we were discussing large and small hot dogs, it could make sense to have halves.

[Daffynition]

[Axenolith]

You know what’s funny, is I “get” that totally looking at your breakdown, particularly at the check your work part, but the logical inconsistency created by “dogs” as a set ending with a fractional algebraic answer seems to screw with the mind.

[Swordmaker]

The number of small dogs would be 42.5.
And the number of large dogs wold be 6.5.

There’d be a bloody mess all over the dog arena. . . and could you imagine the owners of the half-dogs persuading their pets to heel and sit?

"Heel, Fi! Heel!"

And the other:

“Sit, Do, Sit!"