Question

The number of ducks and pigs in a field totals 34. The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, determine how many ducks and how many pigs are in the field. (For each answer, enter an exact number.)

Answer 1

Answer: the number of ducks in the field is 25

the number of pigs in the field is 9

Step-by-step explanation:

Let x represent the number of ducks in the field.

Let y represent the number of pigs in the field.

A duck has one head and a pig also has one head.

The number of ducks and pigs in a field totals 34. This means that

x + y = 34

The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, it means that

2x + 4y = 86 - - - - - - - - - - -- - 1

Substituting x = 34 - y into equation 1, it becomes

2(34 - y) + 4y = 86

68 - 2y + 4y = 86

- 2y + 4y = 86 - 68

2y = 18

y = 18/2 = 9

Substituting y = 9 into x = 34 - y, it becomes

x = 34 - 9 = 25