The farmer in the dell

[pianoplaya16]

A cunning farmer when asked how many sheep he has, replied, " ONe third of my sheep are in the barn, one fifth of my sheep are in the pastuer, 3 times the difference between these 2 numbers equals the amount of newborns. My daughter has one pet." How many sheep does the farmer have?

 

[galactus]

Let x=number of sheep:

\(\displaystyle \L\\\underbrace{\frac{1}{3}x}_{\text{barn}}+\overbrace{\frac{1}{5}x}^{\text{pasture}}+\underbrace{3(\frac{1}{3}x-\frac{1}{5}x)}_{\text{newborn}}+\overbrace{1}^{\text{pet}}=x\)


Solve for x.