document.write( "Question 669208: Find two numbers whose sum is 163 such that when the larger number is divided by the smaller, the quotient is 3 and the remainder is 3. \n" ); document.write( "

Algebra.Com's Answer #416281 by KMST(5328) $\"\"$ $\"About$

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$\"a\"$ = the larger integer
\n" ); document.write( " $\"b\"$ = the smaller integer
\n" ); document.write( "Their sum is 163 translates into $\"a%2Bb=163\"$
\n" ); document.write( "When the larger number is divided by the smaller, the quotient is 3 and the remainder is 3 translates into
\n" ); document.write( " $\"a=3b%2B3\"$ (If you need it, see the explanation below).
\n" ); document.write( "
\n" ); document.write( "You end up with the system
\n" ); document.write( " $\"system%28a%2Bb=163%2Ca=3b%2B3%29\"$
\n" ); document.write( "which can be easily solved by substitution.
\n" ); document.write( "Substituting $\"a=3b%2B3\"$ into $\"a%2Bb=163\"$ you get
\n" ); document.write( " $\"3b%2B3%2Bb=163\"$ <--> $\"4b%2B3=163\"$ <--> $\"4b=163-3\"$ <--> $\"4b=160\"$ <--> $\"4b%2F4=160%2F4\"$ <--> $\"highlight%28b=40%29\"$
\n" ); document.write( "Then, substituting $\"b=40\"$ into $\"a=3b%2B3\"$ we get
\n" ); document.write( " $\"a=3%2A40%2B3\"$ <--> $\"a=120%2B3\"$ <--> $\"highlight%28a=123%29\"$
\n" ); document.write( "
\n" ); document.write( "EXPLANATION OF WHAT DIVISION, QUOTIENT, AND REMAINDER MEAN:
\n" ); document.write( "The quotient is 3.
\n" ); document.write( "That means that $\"b\"$ fits up to 3 times (but not 4 times) into $\"a\"$ ,
\n" ); document.write( "so that $\"3b\"$ is no larger than $\"a\"$ ( $\"3b%3C=a\"$ ),
\n" ); document.write( "but $\"4b\"$ does not fit into $\"a\"$ .
\n" ); document.write( "It is larger, $\"4b%3Ea\"$
\n" ); document.write( "There is a remainder. It is 3.
\n" ); document.write( "It turns out that $\"3b%3Ca\"$ and the difference is the remainder
\n" ); document.write( " $\"a-3b=3\"$ <--> $\"a=3b%2B3\"$ \n" ); document.write( "

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