Difference between revisions of "2018 AMC 8 Problems/Problem 8"
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| − | ==Problem | + | ==Problem== |
| − | Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students. | + | Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students. |
<asy> | <asy> | ||
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<math>\textbf{(A) } 3.50 \qquad \textbf{(B) } 3.57 \qquad \textbf{(C) } 4.36 \qquad \textbf{(D) } 4.50 \qquad \textbf{(E) } 5.00</math> | <math>\textbf{(A) } 3.50 \qquad \textbf{(B) } 3.57 \qquad \textbf{(C) } 4.36 \qquad \textbf{(D) } 4.50 \qquad \textbf{(E) } 5.00</math> | ||
| − | {{AMC8 box|year=2018|num-b= | + | |
| + | ==Solution== | ||
| + | |||
| + | The mean, or average number of days is the total number of days divided by the total number of students. The total number of days is <math>1\cdot 1+2\cdot 3+3\cdot 2+4\cdot 6+5\cdot 8+6\cdot 3+7\cdot 2=109</math>. The total number of students is <math>1+3+2+6+8+3+2=25</math>. Hence, <math>\frac{109}{25}=\boxed{\textbf{(C) } 4.36}</math>. | ||
| + | |||
| + | This problem is a good example of times when the problem statement may give information that may seem important to solving the problem, but turns out it's just there to mess around with you. | ||
| + | |||
| + | ~Nivaar | ||
| + | |||
| + | In my opinion, I think that it's not a good example of that. | ||
| + | |||
| + | ~SuperVince1 | ||
| + | |||
| + | == Video Solution (CRITICAL THINKING!!!)== | ||
| + | https://youtu.be/YUJ29HaLjLo | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/1bkVulggOEw | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | == Video Solution by OmegaLearn == | ||
| + | https://youtu.be/51K3uCzntWs?t=466 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2018|num-b=7|num-a=9}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 08:00, 17 June 2024
Contents
Problem
Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.
![[asy] size(8cm); void drawbar(real x, real h) { fill((x-0.15,0.5)--(x+0.15,0.5)--(x+0.15,h)--(x-0.15,h)--cycle,gray); } draw((0.5,0.5)--(7.5,0.5)--(7.5,5)--(0.5,5)--cycle); for (real i=1; i<5; i=i+0.5) { draw((0.5,i)--(7.5,i),gray); } drawbar(1.0,1.0); drawbar(2.0,2.0); drawbar(3.0,1.5); drawbar(4.0,3.5); drawbar(5.0,4.5); drawbar(6.0,2.0); drawbar(7.0,1.5); for (int i=1; i<8; ++i) { label("$"+string(i)+"$",(i,0.25)); } for (int i=1; i<9; ++i) { label("$"+string(i)+"$",(0.5,0.5*(i+1)),W); } label("Number of Days of Exercise",(4,-0.1)); label(rotate(90)*"Number of Students",(-0.1,2.75)); [/asy]](http://latex.artofproblemsolving.com/f/7/a/f7add6258fd09de75421fb0d08e39071b65b128c.png)
What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia's class?
Solution
The mean, or average number of days is the total number of days divided by the total number of students. The total number of days is 
. The total number of students is 
. Hence, 
.
This problem is a good example of times when the problem statement may give information that may seem important to solving the problem, but turns out it's just there to mess around with you.
~Nivaar
In my opinion, I think that it's not a good example of that.
~SuperVince1
Video Solution (CRITICAL THINKING!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/51K3uCzntWs?t=466
~ pi_is_3.14
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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. 
