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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Since 10% of the students speak neither language, 90% must speak at least one language. Since 72% speak Chinese and 65% can speak English, we know, by [[Principle of Inclusion-Exclusion]], that 72+65-90=47 of the students speak both languages.
  
 
-Potato2017
 
-Potato2017
  
 
==See Also==
 
==See Also==

Revision as of 14:51, 24 June 2020

Problem

In a language college, $72\%$ students can speak Chinese, $65\%$ students can speak English, and $10\%$ students can speak neither Chinese nor English. Find the percentage of students who can speak both Chinese and English.

Solution

Since 10% of the students speak neither language, 90% must speak at least one language. Since 72% speak Chinese and 65% can speak English, we know, by Principle of Inclusion-Exclusion, that 72+65-90=47 of the students speak both languages.

-Potato2017

See Also

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