There were pigs and ducks on a farm. The farmer counted 48 heads and 152 legs. How many pigs and ducks were on the farm?

Answer 1

There were pigs and ducks on a farm. The farmer counted 48 heads and 152 legs. How many pigs and ducks were on the farm?

Assign variables:

Let p = number of pigs

d = number of ducks

Number of pigs heads + number of ducks heads = 48

p + d = 48 [eq1]

Number of pigs legs + number of ducks legs = 152

4p + 2d = 152 [eq2]

You may solve by substitution or elimination.

4p + 4d = 192 [4*eq1]

4p + 2d = 152 [eq2]

------------------------- [elimination; subtract equations]

2d = 40

d = 20

p + d = 48

d = 20

------------------ [elimination; subtract equations]

p = 28

Check:

Does p + d = 48 ?

28 + 20 = 48 ?

48 = 48 ?yes

Does 4p + 2d = 152 ?

4(28) + 2(20) = 152 ?

112 + 40 = 152 ?

152 = 152 ?yes