Question

Farmer Ben has only ducks and cows 24 in total. He can’t remember how many of each he
has. He knows that the animals have a total of 66 legs. Assuming that each animal has all legs intact
and no extra limbs, how many of each animal does farmer Ben have? Draw a clear diagram to answer
this question.


Help ME and plzz show your work thank you love

Answer 1

Ok so you have d ducks and c cows. We know d+c=24. Also, since ducks have 2 legs and cows have 4 legs, 2d+4c=66.

We now have a systems of equations to solve for a variable using elimination

2(d+c=24)
1(2d+4c=66)

2d+2c=24
2d+4c=66

-2c=-18
c=9

Now that we have the number of cows, we can easily find the number of ducks by plugging in 9 to the equation c+d=24

9+d=24
d=15

There are 9 cows and 15 ducks.