1999 CEMC Pascal Problems/Problem 16

Problem

In an election, Harold received $60\%$ of the votes and Jacquie received all the rest. If Harold won by $24$ votes, how many people voted?

$\text{ (A) }\ 40 \qquad\text{ (B) }\ 60 \qquad\text{ (C) }\ 72 \qquad\text{ (D) }\ 100 \qquad\text{ (E) }\ 120$

Solution

Let $p$ be the number of people that voted in total. This means that $60\% \times p = 0.6p$ people voted for Harris, and $p - 0.6p = 0.4p$ people voted for Jacquie.

We know that $0.6p$ must be $0.4p + 24$ from the fact that Harold won by $24$ votes, which gives:

$0.6p = 0.4p + 24$

$0.2p = 24$

$p = \frac{24}{0.2} = \frac{240}{2} = \boxed {\textbf {(E) } 120}$

~anabel.disher

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1999 CEMC Pascal Problems/Problem 16

Problem

Solution