Difference between revisions of "2017 AMC 10B Problems/Problem 11"
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− | The number of people who say they dislike dancing but actually like dancing is, <math>60%*20% = 12%</math>. Then the number of people who say they dislike dancing and actually do dislike dancing is, <math>40%*90% = 36%</math>. After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have <math>\frac{12%}{12% + 36%}</math> which would then be <math>\frac{12%}{48%} | + | The number of people who say they dislike dancing but actually like dancing is, <math>60%*20% = 12%</math>. Then the number of people who say they dislike dancing and actually do dislike dancing is, <math>40%*90% = 36%</math>. After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have <math>\frac{12%}{12% + 36%}</math> which would then be <math>\frac{12%}{48%} = \frac{1}{4}</math> or |
− | <math>\boxed{\textbf{(D)}\ 25%}</math> | + | <math>\boxed{\textbf{(D) }\ 25%}</math> |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}} | {{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:12, 7 January 2021
Problem
At Typico High School, of the students like dancing, and the rest dislike it. Of those who like dancing, say that they like it, and the rest say that they dislike it. Of those who dislike dancing, say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?
Video Solution & Solution
~savannahsolver
The number of people who say they dislike dancing but actually like dancing is, $60%*20% = 12%$ (Error compiling LaTeX. ! Missing $ inserted.). Then the number of people who say they dislike dancing and actually do dislike dancing is, $40%*90% = 36%$ (Error compiling LaTeX. ! Missing $ inserted.). After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have $\frac{12%}{12% + 36%}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) which would then be $\frac{12%}{48%} = \frac{1}{4}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) or $\boxed{\textbf{(D) }\ 25%}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.)
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 AMC 10 Problems and Solutions |
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