document.write( "Question 1068817: If the ratio of newborn girls to boys in a particular hospital is 5 : 3, which of the following could be the number of children in the hospital? \n" ); document.write( "

Algebra.Com's Answer #684059 by KMST(5328) $\"\"$ $\"About$

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The total number of newborn children in the hospital has to be a multiple of $\"5%2B3=8\"$ , such as
\n" ); document.write( "8,16,24,32,...
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\n" ); document.write( "For an algebraic proof:
\n" ); document.write( " $\"B\"$ = number of newborn boys
\n" ); document.write( " $\"G\"$ = number of newborn girls
\n" ); document.write( " $\"G%2FB=5%2F3\"$ <--> $\"3G=5B\"$
\n" ); document.write( "Since $\"B\"$ and $\"G\"$ are whole numbers,
\n" ); document.write( "it is obvious that
\n" ); document.write( " $\"G\"$ is a multiple of $\"5\"$
\n" ); document.write( "(let's say $\"G=5g\"$ , with $\"g\"$ being a whole number),
\n" ); document.write( "and it is equally obvious that
\n" ); document.write( " $\"B\"$ is a multiple of $\"3\"$
\n" ); document.write( "(let's say $\"B=3b\"$ , with $\"b\"$ being a whole number).
\n" ); document.write( "Now, substituting those expressions for $\"B\"$ and $\"G\"$ in $\"3G=5B\"$ ,
\n" ); document.write( "we get $\"3%285g%29=5%283b%29\"$ ---> $\"15g=15b\"$ ---> $\"g=b\"$ .
\n" ); document.write( "Now the total number of newborn children in the hospital is $\"B%2BG\"$ ,
\n" ); document.write( "and since $\"system%28G=5g%2CB=3b%2C%22and%22%2Cg=b%29\"$ ,
\n" ); document.write( " $\"B%2BG=5g%2B3b=5b%2B3b=8b\"$ .
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