The number of ducks and cows in a field totals 35. The total number of legs among them is 98. Assuming each duck has exactly two legs and each cow has exactly four legs, determine how many ducks and how many cows are in the field.
d = number of ducks
c = number of cows
The number of ducks and cows in a field totals 35 means:
d + c = 35
Assuming each duck has exactly two legs and each cow has exactly four legs, the total number of legs among them is 98 means:
2 d + 4 c = 98
Now you must solve system of equations:
d + c = 35
2 d + 4 c = 98
Multiply both sides of first equation by 2.
2 d + 2 c = 70
Subtract the second equation from this equation.
2 d + 2 c = 70
-
2 d + 4 c = 98
___________
2 d - 2 d + 2 c - 4 c = 70 - 98
- 2 c = - 28
c = - 28 / - 2
c = 14
Put this value in equation d + c = 35
d + 14 = 35
d = 35 - 14 = 21
21 ducks and 14 cows