A farm has pigs and turkeys. In total, there are 35 heads and 116 paws

Question

A farm has pigs and turkeys. In total, there are 35 heads and 116 paws. How many pigs are there on the farm?

A. 12
B. 15
C. 17
D. 21
E. 23

aritrar4 · Answer

Let x be no. of turkeys and y be no. of pigs

So, x + y = 35 (heads)
2x + 4y = 116 (paws)

So, x = 12 and y = 23

So no. of pigs = 23. Option E

BrentGMATPrepNow · Answer

Let P = the total number of pigs
Let T = the total number of turkeys

Pigs and turkeys have 1 head each. So, we can write:  P + T = 35 
A pig has 4 paws, and a turkey has 2 paws. So we can write:  4P + 2T = 116

We now have the following system: 
 4P + 2T = 116 
 P + T = 35

Take the bottom equation, and multiply both sides by 4 to get the equivalent equation: 
 4P + 2T = 116 
 2P + 2T = 70

Subtract the bottom equation from the top equation to get: 2P = 46
Solve: P = 23

Answer: E

Cheers,
Brent

Archit3110 · Answer

given
x+y=35
2x+4y=116
x+2y=58
x+y=35
solve for x& y ; x = 23
option e

Kinshook · Answer

Given: A farm has pigs and turkeys. In total, there are 35 heads and 116 paws. 
Asked: How many pigs are there on the farm?

Let the number of pigs in the farm be x
Number of turkeys = 35 - x

Number of paws = 4x + 2(35-x) = 116
2x + 70 = 116
2x = 46
x = 23

IMO E

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