2000 PMWC Problems/Problem I5

Revision as of 14:50, 24 June 2020 by Potato2017 (talk | contribs) (Solution)

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

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