Question Number 52741 by Otchere Abdullai last updated on 12/Jan/19
$$\: \\ $$$${please}\:{help}\:{me}\:{solve}\:{this}\:{question}\:{sir}. \\ $$$$\mathrm{I}{n}\:{a}\:{survey}\:{of}\:\:\mathrm{100}\:{out}-{patients}\:{who}\: \\ $$$${reported}\:{at}\:{the}\:{hospital}\:{one}\:{day},\:{It}\: \\ $$$${was}\:{found}\:{out}\:{that}\:\mathrm{70}\:{coplained}\:{of}\: \\ $$$${fever},\:\mathrm{50}\:{complained}\:{of}\:{stomach}\: \\ $$$${ache}\:{and}\:\mathrm{30}\:{were}\:\:{injured}.\:{All}\:\: \\ $$$${patients}\:{had}\:{at}\:{least}\:{one}\:{of}\:{the}\: \\ $$$${complaints}\:{and}\:\mathrm{44}\:{had}\:{exactly}\:{two}\: \\ $$$${of}\:{the}\:{complaints}.\:{How}\:{many}\:{had}\:{all}\: \\ $$$${complaints}? \\ $$
Answered by mr W last updated on 12/Jan/19
$${A}...={patients}\:{with}\:{exact}\:{one}\:{complaint} \\ $$$${B}...={patients}\:{with}\:{exact}\:{two}\:{complaints} \\ $$$${C}={patients}\:{with}\:{all}\:{three}\:{complaints} \\ $$$${A}_{\mathrm{1}} +{B}_{\mathrm{1}} +{B}_{\mathrm{3}} +{C}=\mathrm{70}\:\:\:...\left(\mathrm{1}\right) \\ $$$${A}_{\mathrm{2}} +{B}_{\mathrm{1}} +{B}_{\mathrm{2}} +{C}=\mathrm{50}\:\:\:...\left(\mathrm{2}\right) \\ $$$${A}_{\mathrm{3}} +{B}_{\mathrm{2}} +{B}_{\mathrm{3}} +{C}=\mathrm{30}\:\:\:...\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{1}\right)+\left(\mathrm{2}\right)+\left(\mathrm{3}\right): \\ $$$${A}_{\mathrm{1}} +{A}_{\mathrm{2}} +{A}_{\mathrm{3}} +\mathrm{2}\left({B}_{\mathrm{1}} +{B}_{\mathrm{2}} +{B}_{\mathrm{3}} \right)+\mathrm{3}{C}=\mathrm{150}\:\:\:...\left(\mathrm{4}\right) \\ $$$${A}_{\mathrm{1}} +{A}_{\mathrm{2}} +{A}_{\mathrm{3}} +{B}_{\mathrm{1}} +{B}_{\mathrm{2}} +{B}_{\mathrm{3}} +{C}=\mathrm{100}\:\:\:...\left(\mathrm{5}\right) \\ $$$$\left(\mathrm{4}\right)−\left(\mathrm{5}\right): \\ $$$${B}_{\mathrm{1}} +{B}_{\mathrm{2}} +{B}_{\mathrm{3}} +\mathrm{2}{C}=\mathrm{50}\:\:\:\:...\left(\mathrm{6}\right) \\ $$$${B}_{\mathrm{1}} +{B}_{\mathrm{2}} +{B}_{\mathrm{3}} =\mathrm{44}\:\:\:\:...\left(\mathrm{7}\right) \\ $$$$\left(\mathrm{6}\right)−\left(\mathrm{7}\right): \\ $$$$\mathrm{2}{C}=\mathrm{6} \\ $$$$\Rightarrow{C}=\mathrm{3} \\ $$$${i}.{e}.\:{three}\:{patients}\:{have}\:{all}\:{complaints}. \\ $$
Commented by mr W last updated on 12/Jan/19
Commented by Otchere Abdullai last updated on 12/Jan/19
$${God}\:{richly}\:{bless}\:{you}\:{sir}\:{infact}\:{if}\: \\ $$$${there}\:{is}\:{something}\:{greater}\:{than}\: \\ $$$${blessing}\:{thus}\:{what}\:{i}\:{pray}\:{for}\:{you}\:{sir} \\ $$
Commented by mr W last updated on 12/Jan/19
$${thank}\:{you}\:{sir}! \\ $$