2017 AMC 8 Problems/Problem 2
Contents
Problem
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 
votes, then how many votes were cast all together?
![[asy] draw((-1,0)--(0,0)--(0,1)); draw((0,0)--(0.309, -0.951)); filldraw(arc((0,0), (0,1), (-1,0))--(0,0)--cycle, lightgray); filldraw(arc((0,0), (0.309, -0.951), (0,1))--(0,0)--cycle, gray); draw(arc((0,0), (-1,0), (0.309, -0.951))); label("Colby", (-0.5, 0.5)); label("25\%", (-0.5, 0.3)); label("Alicia", (0.7, 0.2)); label("45\%", (0.7, 0)); label("Brenda", (-0.5, -0.4)); label("30\%", (-0.5, -0.6)); [/asy]](http://latex.artofproblemsolving.com/7/b/7/7b7b4b1940b8afd1669156f092481dd6fc6f5a83.png)
Solution 1
Let 
be the total amount of votes casted. From the chart, Brenda received 
of the votes and had votes. We can express this relationship as 
. Solving for , we get 
Solution 2
We're being asked for the total number of votes cast -- that represents 
of the total number of votes. Brenda received votes, which is 
of the total number of votes. Multiplying by 
we get the total number of votes, which is 
Solution 3
If votes is 
of all the votes, we can divide that by 
to get 
as 10%, and then we can multiply the by 
to get to 
.
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See Also
| 2017 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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