There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?

To solve this problem, we can set up an equation based on the information given.

Let's denote the number of large dogs as x. According to the problem, the number of small dogs is 36 more than the number of large dogs, so we can denote the number of small dogs as x + 36.

The total number of dogs is the sum of the number of large dogs and the number of small dogs, which is 49 according to the problem. So we can set up the following equation:

x + (x + 36) = 49

Solving this equation will give us the number of large dogs (x) and the number of small dogs (x + 36).

First, combine like terms on the left side of the equation:

2x + 36 = 49

Next, subtract 36 from both sides of the equation to isolate the term with x:

2x = 49 - 36 2x = 13

Finally, divide both sides of the equation by 2 to solve for x:

x = 13 / 2 x = 6.5

However, the number of dogs must be a whole number, so it's not possible to have 6.5 large dogs. This suggests that there might be a mistake in the problem. If we assume that there are 7 large dogs and 42 small dogs, the problem makes sense because 7 + 42 = 49 and 42 - 7 = 35, which is close to the 36 more small dogs than large dogs stated in the problem. So, there are likely 42 small dogs signed up to compete.