Difference between revisions of "2000 PMWC Problems/Problem I5"
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==Solution== | ==Solution== | ||
| + | Since <math>10 \text{%}</math> of the students speak neither language, <math>90 \text{%}</math> must speak at least one language. Since <math>72 \text{%}</math> speak Chinese and <math>65 \text{%}</math> can speak English, we know, by [[Principle of Inclusion-Exclusion]], that <math>72+65-90=\boxed{47%}</math> of the students speak both languages. | ||
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| + | -Potato2017 | ||
==See Also== | ==See Also== | ||
Revision as of 13:50, 24 June 2020
Problem
In a language college, 
students can speak Chinese, 
students can speak English, and 
students can speak neither Chinese nor English. Find the percentage of students who can speak both Chinese and English.
Solution
Since $10 \text{%}$ (Error compiling LaTeX. Unknown error_msg) of the students speak neither language, $90 \text{%}$ (Error compiling LaTeX. Unknown error_msg) must speak at least one language. Since $72 \text{%}$ (Error compiling LaTeX. Unknown error_msg) speak Chinese and $65 \text{%}$ (Error compiling LaTeX. Unknown error_msg) can speak English, we know, by Principle of Inclusion-Exclusion, that $72+65-90=\boxed{47%}$ (Error compiling LaTeX. Unknown error_msg) of the students speak both languages.
-Potato2017
