SAT Math: Percent Word Problems
Here is a tricky SAT question from the October 2006 exam.
In an election, 2.8 million votes were cast and each vote was for Candidate I or Candidate II. Candidate I received 28,000 more votes than Candidate II. What percent of the 2.8 million votes were cast for Candidate I?
(A) 50.05%
(B) 50.1%
(C) 50.5%
(D) 51%
(E) 55%
Begin by asking yourself a) what do I already know? and b) what do I need to know? In this case, we already know the number of total votes cast = 2.8 million, and we know that Candidate I received 28,000 more votes than Candidate II. We need to know the percent of votes cast for Candidate I. The percent of votes cast for Candidate I is the number of votes cast for him/her divided by the total number of votes cast. We already know the total number of votes cast, so we only need to know the number of votes cast for Candidate I.
Can we write an equation to figure out the number of votes cast for Candidate I? Let’s call that number x.
Let x = the number of votes cast for Candidate I
x – 28,000 = the number of votes cast for Candidate II (since candidate I received 28,000 more).
x + (x – 28,000) = 2,800,000
2x – 28,000 = 2,800,000
2x = 2,828,000
x = 1,414,000
Now we only need to figure out what percent of the total 1,414,000 represents. Remember that percent is part/whole, so the percent of votes Candidate I receives is 1,414,000/2,800,000, which is 0.505, or 50.5%
Don’t make the mistake of oversimplifying this problem (as many students did) and figuring out that 28,000 votes is 1% of the total. This is true, but it does not mean that Candidate I received 51% of the votes. If you are performing only one step to solve a problem near the end of the section, you are definitely oversimplifying it.
