Create a Venn diagram with the information given. Be sure to label each circle. $\newline$ There are $28$ dogs are in a kennel with the following characleristics: $\newline$ - $11$ of the dogs are brown. $\newline$ - $8$ of the dogs have short tails. $\newline$ - $17$ of the dogs have long hair. $\newline$ - There is only one dog that is brown with a short tail and long hair. $\newline$ - $3$ of the dogs are brown with short tails and do not have long hair. $\newline$ - $3$ of the dogs have short tails and long hair but are not brown. $\newline$ If all of the dogs in the kennel have at least one of the mentioned characteristics, how many dogs are brown with long hair but do not have short tails? $\qquad$

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Grade 8

Solve a system of equations using elimination: word problems

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Q. Create a Venn diagram with the information given. Be sure to label each circle.

\newline

There are

28

dogs are in a kennel with the following characleristics:

\newline

11

of the dogs are brown.

\newline

8

of the dogs have short tails.

\newline

17

of the dogs have long hair.

\newline

- There is only one dog that is brown with a short tail and long hair.

\newline

3

of the dogs are brown with short tails and do not have long hair.

\newline

3

of the dogs have short tails and long hair but are not brown.

\newline

If all of the dogs in the kennel have at least one of the mentioned characteristics, how many dogs are brown with long hair but do not have short tails?

\qquad

Find Brown Dogs: First, let's find the number of dogs that are brown and have long hair. We know there's one dog that has all three characteristics: brown, short tail, and long hair. $\newline$ $11$ brown dogs $- 1$ dog with all characteristics $= 10$ dogs that are brown and might have long hair or short tails.
Subtract Short Tails: Now, let's subtract the $3$ brown dogs with short tails that do not have long hair from the $10$ dogs we just found. $\newline$ $10$ dogs (brown, might have long hair or short tails) $-$ $3$ dogs (brown with short tails and no long hair) $=$ $7$ dogs that are brown and have long hair or short tails.
Identify Long Hair: We need to find the number of brown dogs with long hair but without short tails. We already know there are $3$ dogs with short tails and long hair but are not brown, so they are not included in the brown dogs count. $\newline$ $7$ dogs (brown with long hair or short tails) - $1$ dog (brown with short tail and long hair) = $6$ dogs that are brown with long hair but do not have short tails.