A student is collecting signatures for a petition to change an unfavorable school rule. One lunch shift the student collected 70 signatures. This is the signatures required for the petition. How many signatures did the student need?

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.