# JOhn has ducs and pigs in one pen with a total of 40 legs in the pen. If john has 3 times the pigs than he has the ducks how many pigs does he have?

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### 1 Answer

Let the number of ducks in John’s pen be x.

The number of pigs is 3*x = 3x.

A duck has two legs, and a pig has four.

Therefore, total number of legs in his pen is:

x*2 + 3x*4 = 2x+12x = 14x

By the condition of the problem,

14x = 40

x = 40/14 = 20/7 = 6 6/7

This is a fraction. John can not have a fractional number of living beings; be it a duck or a pig in his pen.

**So there must be something wrong with the statement of the problem.**

(Assuming that john has 3 times the ducks than he has the pigs, then total number of legs in his pen would be:

3x*2+x*4 = 6x+4x = 10x

and, the problem would then require,

10x = 40

x = 4

Number of ducks = 12, number of pigs = 4)

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That is what I thought. I thought I had something wrong or the instructor just wanted to throw me off by partial pigs and ducks. Maybe, a little short legged? :)