Need help with 4th grade word problem

[lamberts76]

Hi, I could really use some help explaining to my son how to do his homework problem.


While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give you a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store?

Please explain how you found the answer.
Thanks.

 

[Mrspi]

Hi, I could really use some help explaining to my son how to do his homework problem.


While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give you a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store?

Please explain how you found the answer.
Thanks.

Since this is stated to be a 4th grade problem, I would suggest a 4th-grade approach to solving it.

Elementary school students study various problem-solving strategies, one of which is sometimes called the "guess and check" method.

Let's see how that would work on your problem. There are 16 animal heads, and that would tell us there must be 16 animals (since each animal has ONE head). Let's guess that there are 8 birds and 8 cats.

Now that we've made a guess, we need to check to see if the rest of the conditions of the problem are satisfied. We have guessed that there are 8 birds, and since each bird has two feet, there must be 8 X 2 or 16 feet belonging to the birds. We've guessed that there are 8 cats, and since each cat has 4 feet, there must be 8 X 4, or 32 feet belonging to the cats. 16 feet + 32 feet gives us 48 feet. That's too many feet! So, we need to adjust our guess. If we have too many feet with our first guess, we need to reduce the number of cats, and increase the number of birds.

We can make a new guess....maybe 9 birds and 7 cats. Check to see how many feet THAT gives. If it is still not 42 feet, you'll need to adjust your guess again.

For students who have not studied algebra (particularly equations involving two variables!) this method works nicely. And as a bonus, it helps students get a sense of when an answer is reasonable.

 

[Deleted member 4993]

Hi, I could really use some help explaining to my son how to do his homework problem.


While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give you a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store?

Please explain how you found the answer.
Thanks.

For fourth grade - "educated" trial and error method is best.

Since we have no idea in the begining - we start with equal birds and cats.

So our first guess is 8 cats and 8 birds. How feet do we have - 8 * 4 + 8 * 2 = 48

Too many feet. Notice that if we replace 1 cat with 1 bird - we lose 2 feet. we need to lose 6 feet - lose 3 cats and get 3 more birds. So next guess would be 5 cats and 11 birds. We still have 16 heads (no mutants) - and we have (5 * 4 + 11 * 2 =) 42 feet.

Problem solved.....