Calvin and Susie are running for class president. Of the first 80% of the ballots that are counted, Susie receives 53% of the votes and Calvin receives 47%. At least what percentage of the remaining votes must Calvin receive to catch up to Susie in the election?
Let V be the total number of votes. 80% = 0.8, so 0.8V votes have been counted.
Susie has 53% of this, which is (0.53)(0.8V).
Calvin has 47% of this, which is (0.47)(0.8V).
The difference between their counts is (0.53)(0.8V) – (0.47)(0.8V) = (0.06)(0.8V) = 0.048V.
The remaining votes make up 20% of V, or 0.2V.
Divide the amount Calvin needs by the remaining amount: 0.048V / 0.2V = 0.24, or 24%.
My answer was wrong, it's actually 62% can anyone please help me understand what I did wrong and how to do this problem?
Best Answer
Calvin has received $0.47\cdot 0.8V = 0.376V$ votes, but he needs $0.5V$ total votes to catch up. Thus of the remaining $0.2V$, he needs $0.124V$ votes, so the percentage is $0.124/0.2 = 0.62$.
Your mistake was assuming that if Calvin receives a number of votes that allows him to catch up to Susie's current total, he will win. But surely Susie gets some of those $0.2V$ votes as well.