27 guest samantha gathered the following information on a given day at the dog park. • there are 32 dogs…
27 guest samantha gathered the following information on a given day at the dog park. • there are 32 dogs playing at the dog park. • 15 of the dogs are puppies. • 11 of the dogs are not puppies and have long hair. • there are 6 more dogs that have long hair than dogs that do not have long hair. fill in the table completely to represent samantha’s data.
Answer
Explanation:
Step1: Find number of non - long - hair dogs
Let the number of dogs with long hair be $x$ and the number of dogs without long hair be $y$. We know that $x + y=32$ and $x=y + 6$. Substitute $x$ in the first equation: $(y + 6)+y=32$. Combine like terms: $2y+6 = 32$. Subtract 6 from both sides: $2y=32 - 6=26$. Divide by 2: $y = 13$, so $x=y + 6=19$.
Step2: Find number of long - hair puppies
We know that the number of non - puppies with long hair is 11 and the total number of long - hair dogs is 19. So the number of long - hair puppies is $19-11 = 8$.
Step3: Find number of non - long - hair puppies
The total number of puppies is 15. Since 8 puppies have long hair, the number of non - long - hair puppies is $15 - 8=7$.
Step4: Find number of non - long - hair non - puppies
The number of non - long - hair dogs is 13. Since 7 non - long - hair dogs are puppies, the number of non - long - hair non - puppies is $13 - 7 = 6$.
| Dogs That are Puppies | Dogs That are Not Puppies | Total | |
|---|---|---|---|
| Dogs with Long Hair | 8 | 11 | 19 |
| Dogs That Do Not Have Long Hair | 7 | 6 | 13 |
| Total | 15 | 17 | 32 |
Answer:
| Dogs That are Puppies | Dogs That are Not Puppies | Total | |
|---|---|---|---|
| Dogs with Long Hair | 8 | 11 | 19 |
| Dogs That Do Not Have Long Hair | 7 | 6 | 13 |
| Total | 15 | 17 | 32 |