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Answer:

We are given the following information:

- 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.

We are asked to find out how many small dogs are signed up to compete.

To solve this problem, we can use the following steps:

- Let x be the number of large dogs signed up to compete.
- The number of small dogs signed up to compete is x+36.
- The total number of dogs signed up to compete is x+(x+36)=2x+36.
- We are given that the total number of dogs signed up to compete is 49, so we can set up the following equation: 2x+36=49.
- Solve the equation for x.
- Once we know the number of large dogs, we can find the number of small dogs by adding 36.

Steps to solve: **1. Let x be the number of large dogs signed up to compete.** x

**2. The number of small dogs signed up to compete is x+36.** x+36

**3. The total number of dogs signed up to compete is x+(x+36)=2x+36.** 2x+36

**4. We are given that the total number of dogs signed up to compete is 49, so we can set up the following equation: 2x+36=49.** 2x+36=49

**5. Solve the equation for x.** 2x=13 x=6.5

**6. Once we know the number of large dogs, we can find the number of small dogs by adding 36.** x+36=6.5+36 x=42.5

**Answer:** There are 42.5 small dogs signed up to compete.