Question

there are 49 dogs signed up to compete in the dog show? there are 36 more small dogs singed up to compete. how many small dogs are signed up to compete

Answer 1

Number of small dogs signed up to compete is 42.5. This is not possible as 0.5 dogs doesn't make sense. The data given could be wrong, in that case you can follow the same procedure and replace the data.

Explanation:

We can do this by building an equation.

Lets take the number of small dogs is
`x`

Then,

The number of Large dogs will be
`x-36`

The total number of dogs signed up is given as 49.

Therefore,

Number of Small Dogs + Number of Large Dogs = 49

⇒
`x+(x-36)=49`

=
`2x-36=49`

=
`2x=49+36`

=
`2x=85`

=
`x=42.5`

Therefore, number of small dogs signed up to compete is 42.5. This is not possible as 0.5 dogs doesn't make sense. The data given could be wrong, in that case you can follow the same procedure and replace the data.

Answer 2

Most people do this king of problem stating a system of two equations with two variables.

I will work with one variable, because this will show you to save time and leave you more time to solve more problems.

1) Call x the number of non-small dogs.

2) Given that there are 36 more small dogs than non-small dogs, the number of small dogs is 36 + x

3) And the total number of dogs is x + (36 +x )

4) That is equal to 49 dogs, so you set the equation:

x + 36 + x = 49

5) Solve the equation:

2x + 36 = 49
2x = 49 - 36
2x = 13
x = 13/2
x = 6.5

And the number of small dogs would be 36 + x = 36 + 6.5 = 42.5

Of course, the absurd result (42 and half small dogs) is product of an unfortunate selection of numbers for the hypothetical situation.

The important thing is to understand the procedure, and that you always have to analyze the result.