Help Solve Math Problem

Hi Ellen,

2 feet per chicken (x)
4 feet per pig (y)

2x + 4y = 70 feet
x + y = 26 heads

x= 26-y

**plug our new value for x (26-y)into the first formula:

2(26-y) + 4y =70
52-2y +4y = 70
52 +2y = 70
2y=70-52
2y= 18
y = 9

x +9 = 26
x= 26-9
x = 17

ANSWER: 9 pigs and 17 chickens
(you could also solve for x first and then plug it into the x+y=26 for y.) Hope this helps. send me a message if you have a question.
A.

3 moms found this helpful

Do not use algebra for this problem. Children do not learn true algebra until sixth grade. The way you would work this problem is with using pictures and guessing. This is a problem solving type of question.

You start out by guessing. For example, I think there are 14 pigs, each with 4 feet. When multiplied that would equal 56. Then guess how many chickens. For example 7 chickens each with two feet, which equals 14. Then add the two 56 + 14 = 70. The problem with this is the feet are correct, but the number of animals is incorrect. You keep guessing until you come up with the right answer which is 9 pigs and 17 chickens. This is a total of 26 animals and a total of 70 legs. Fourth graders use pictures, multiplication, and addition for this type of problem. You can check you answer by drawing a picture.
Good Luck. This type of problem is objective six on the TAKS test, which is high level thinking.

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You can also solve this problem by drawing a picture. This may help your son to understand it a little easier. I taught 4th grade and my studnets had this "classic problem". First draw 26 circles for heads. Then you know that pigs have 4 legs and chickens have 2. So, now have your son draw 2 legs(sticks) on each head. Have him count the legs and he will find that he has used 52 of the 70 legs. Now have him subtract the 52 legs from the original 70 and he will see that there are 18 legs left. So now you talk about horses having 4 legs so he will go back and add 2 more legs to each head until he has used the 18 remaining legs. Then you count the 4 legged animals and you get 9 and the 2 legged animals and you get 17. To check it mathematically: 9 horses + 17 chickens=26 heads. 36 horse legs and 34 chicken legs=70 legs.

It seems like a lot of steps, but it is really early in the year for you to expect your son to be able to work it out using multiplication. Drawing a picture helps them to really see and understand the problem.

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Assuming the answer is 9 pigs and 17 chickens, here is how to logically approach it.

If all of the heads were chickens, there would be only 52 feet because each chicken has 2 feet (2*26 = 52).
Since there are 70 feet, subtract 52 from 70 to find that there are 18 extra feet (70-52=18).
Since each pig has 2 extra feet, we divide 18 by 2 to determine the number of pigs (18/2 = 9).
Then we subtract 9 from 26 to determine the number of chickens (26-9 = 17).
So there are 9 pigs and 17 chickens.

You can approach it from the pigs as well and the answers would also come out.

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x = number of chickens
y = number of pigs

so, x + y = 26 animans
and 2x + 4y = 70 (since if you multiply the number of chickens by 2 legs and the number of pigs by 4 legs, you get 70 legs)

x + y = 26 (subtract y from both sides)
x = 26-y (then substitute this in other equation)

2(26-y) + 4y = 70
52-2y+4y=70
52+2y=70
2y=18
y=9

so there are 9 pigs

x+y=26
x+9=26
x=17
so there are 17 chickens

9 pigs times 4 legs = 36 legs
17 chickens time 2 legs = 34 legs
total of 70 legs

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I am not sure how old he is. If he can't exactly write algebraic equations, then he can always draw a picture. While this is a long problem solving strategy, it is a useful one, and it will help him understand it.

1 mom found this helpful