Difference between revisions of "2017 AMC 8 Problems/Problem 2"
(Created page with "Make an equation which states 0.3x=36. When you solve this equation you get x=120, hence the answer (E)") |
Hashtagmath (talk | contribs) |
||
(19 intermediate revisions by 11 users not shown) | |||
Line 1: | Line 1: | ||
− | + | ==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 36 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> | ||
+ | |||
+ | <math>\textbf{(A) }70 \qquad \textbf{(B) }84 \qquad \textbf{(C) }100 \qquad \textbf{(D) }106 \qquad \textbf{(E) }120</math> | ||
+ | |||
+ | ==Solution 1== | ||
+ | |||
+ | Let <math>x</math> be the total amount of votes casted. From the chart, Brenda received <math>30\%</math> of the votes and had <math>36</math> votes. We can express this relationship as <math>\frac{30}{100}x=36</math>. Solving for <math>x</math>, we get <math>x=\boxed{\textbf{(E)}\ 120}.</math> | ||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | We're being asked for the total number of votes cast -- that represents <math>100\%</math> of the total number of votes. Brenda received <math>36</math> votes, which is <math>\frac{30}{100} = \frac{3}{10}</math> of the total number of votes. Multiplying <math>36</math> by <math>\frac{10}{3},</math> we get the total number of votes, which is <math>\boxed{\textbf{(E)}\ 120}.</math> | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/cY4NYSAD0vQ | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2017|num-b=1|num-a=3}} | ||
+ | |||
+ | {{MAA Notice}} |
Revision as of 13:58, 18 January 2021
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 36 votes, then how many votes were cast all together?
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
Video Solution
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.