A farm raises pigs chickens the farmer has total of 102animals one day he counts the legs of all his animals and realizes he has a total of 298 legs how many pigs does the farmer have

The number of pigs the farmer has is 47

Step-by-step explanation:

Assume that the number of pigs is x and the number of chickens is y

∵ The farmer has 102 animals

∵ The number of pigs is x

∵ The number of chickens is y

→ Add them and equate the sum by 102

∴ x + y = 102 ⇒ (1)

∵ Each pig has 4 legs

∴ The number of legs of all pigs is 4x

∵ Each chicken has 2 legs

∴ The number of legs of all chickens is 2y

∵ He has a total of 298 legs

→ Add 4x and 2y, then equate the sum by 298

∴ 4x + 2y = 298 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by -2 to make the coefficients of y equal in values

   and opposite in signs

∵ -2(x) + -2(y) = -2(102)

∴ -2x - 2y = -204 ⇒ (3)

→ Add equations (2) and (3)

∵ (4x + -2x) + (2y + -2y) = (298 + -204)

∴ 2x + 0 = 94

∴ 2x = 94

→ Divide both sides by 2 to find x

∴ x = 47

∴ The number of pigs the farmer has is 47