Difference between revisions of "2000 PMWC Problems/Problem I5"

(Created page with "==Problem== In a language college, <math>72\%</math> students can speak Chinese, <math>65\%</math> students can speak English, and <math>10\%</math> students can speak neither Ch...")
 
(Solution)
Line 3: Line 3:
  
 
==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.
 +
 +
-Potato2017
  
 
==See Also==
 
==See Also==

Revision as of 14:50, 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 $10 \text{%}$ (Error compiling LaTeX. ! File ended while scanning use of \text@.) of the students speak neither language, $90 \text{%}$ (Error compiling LaTeX. ! File ended while scanning use of \text@.) must speak at least one language. Since $72 \text{%}$ (Error compiling LaTeX. ! File ended while scanning use of \text@.) speak Chinese and $65 \text{%}$ (Error compiling LaTeX. ! File ended while scanning use of \text@.) can speak English, we know, by Principle of Inclusion-Exclusion, that $72+65-90=\boxed{47%}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.) of the students speak both languages.

-Potato2017

See Also

Invalid username
Login to AoPS