2017 AMC 8

Complete problem set with solutions and individual problem pages

Problem 2 Easy

Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?

  • A.

    70

  • B.

    84

  • C.

    100

  • D.

    106

  • E.

    120

Answer:E

Solution 1

Let x be the total amount of votes casted. From the chart, Brenda received 30\% of the votes and had 36 votes. We can express this relationship as \frac{30}{100}x=36. Solving for x, we get x=\boxed{\textbf{(E)}\ 120}.

 

Solution 2

We're being asked for the total number of votes cast -- that represents 100\% of the total number of votes. Brenda received 36 votes, which is \frac{30}{100} = \frac{3}{10} of the total number of votes. Multiplying 36 by \frac{10}{3}, we get the total number of votes, which is \boxed{\textbf{(E)}\ 120}.

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