# 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 14:50, 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. ! 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