Farmer Ben has only ducks and cows. He can't remember how many each he has, but he really doesn't need to remember. He does know that he has 22 animals, which is his age. He also remembers that those animals have a total of 56 legs, which is his father's age. Assuming that each animal is normal, how many of each does Farmer Ben have?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. Suppose he's got D ducks and C cows. Then we know that D + C = 22.
    Now: a duck has two legs, and a cow has four. So 2D + 4C = 56, which is the total number of legs. But D + C = 22, so 2D + 2C = 44. So if you subtract this equation from the one that tells you the number of legs, you'll get 2C = 56-44 = 12, so C = 6. But D + C = 22, so D = 16.
    Check it: If C = 6 and D = 16, then D + C = 22, and 2D + 4C = 32 + 24 = 56. Correct.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. 16

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra 1

    a farmer raises chickens and cows. there are 34 animals in all. the farmer counts 110 legs total on these animals. how many chickens and how many cows are on this farm?

  2. Math

    Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling? 20kgs?

  3. math

    on a farm, there are some cows and some chickens. if the animals have a total of 40 heads and 112 legs, how many cows are there?

  4. math

    a farmer has cows and chickens. he has a total of 20 heads and 64 legs. How much of each animal does he have?

  1. science

    Which of the following is an example of inbreeding? A) a farmer chooses the cos in his or her herd that produce he most milk and breeds only those cows. b) a farmer chooses the cows in his or herd that produces the most milk and

  2. Maths

    A farmer finds that he can buy 5 sheep and 5 cows for $129 or 10 sheep and 17 cows for $ much will it cost him to buy 3 sheeps and 2 cows?

  3. Maths

    A farm rears 9 ducks and cows in his farm. There are 28 legs altogether.How many ducks are there in the farm?

  4. algebra

    there were some ducks in the pond.Twenty-eight ducks flew away. Seven more arrived at the pond. Now there are 43 ducks in the pond. How many ducks were in the pond to start?

  1. Math

    A famer has 50 sheep and 20 cows.Calculate the fraction of his animals that are cows.

  2. math

    There are four different kinds of animals on the farm. There is a different number of each kind of animal.There are 19 more cows than sheep. There 19 more ducks than hens. There are more hens than cows.Write a subtraction problem

  3. Calculus

    A farmer has 120 meters of wire fencing to make enclosures for his pigs and cows. The rectangular enclosure he is considering will have one side up against a barn (in the center of one side that is 150 meters long, so the

  4. maths(percentage)

    A village lost 15% of it's cows in a flood and 10% of the remainder died of diseases. If no. Of cows were left now is 7650 what was the original no of cows before the flood ?

View more similar questions or ask a new question.