SOLUTION
In this question, we were given that 50% of the entries are livestock.
Of the entries, we have that 80 % were sold at auction.
Now, let the total number of entries = x
So that :
[tex]\begin{gathered} \frac{50}{100}\text{ x }\frac{80}{100}\text{ x X = 140} \\ =\text{ }\frac{4000\text{ x}}{10000}\text{ = 140} \\ \\ \text{cross}-\text{ multiply , we have that:} \\ 4000\text{ x = 10000 x 140} \\ x\text{ = }\frac{10000\text{ x 140}}{4000} \\ \text{ x= 350} \end{gathered}[/tex]CONCLUSION: There were 350 total entries at the fair.