Question

A student has surveyed 25 voters. Fifteen of these voters indicated that they plan to vote for the governor for re-election. What is the minimal number of additional voters that the student must survey so that 75% of those surveyed plan to vote for the governor for re-election?

Answer 1

Right now, you have \[\frac{15}{25}\] planning to vote for re-election. To satisfy the request, that ratio must equal 75% or 75/100 or 3/4. Adding some number \((x)\) of additional voters will give the minimum, assuming they all plan to vote for re-election:

\[\frac{15+x}{25+x} = \frac{3}{4}\]We add \(x\) to both the numerator and denominator because each additional voter increases both quantities by 1. You can solve for \(x\) by cross-multiplying the two fractions.