280
1) Given that 70 signatures are equivalent to 1/5 of the total, then let's find how many signatures are equivalent to 4/5. Since the student collected 1/5 of those let's find out how many he/she needed.
Since the question does not mention any percentage we'll assume that the student needs the signatures of everyone to decide that matter.
5/5 = 1/5 + 4/5
1 = 1/5 +4/5
2) Writing this as a proportion:
signatures students
70 1/5
x ---------------------------4/5
[tex]\begin{gathered} 70\text{ --------- }\frac{1}{5} \\ x\text{ --------- }\frac{4}{5} \\ 70\times\frac{4}{5}=\frac{1}{5}x \\ 56=\frac{1}{5}x\text{ x5} \\ 280=x \end{gathered}[/tex]3) So the number of signatures needed was 280 since the whole school had 350 students. And 350 signatures yes or no would decide that.