document.write( "Question 756514: if 8 students are seated on each bench, 3 benches are left over. if 5 students are seated on each bench, 12 students are left over. How many benches, students are left over? \n" ); document.write( "

Algebra.Com's Answer #460245 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+n+\"$ = number of students
\n" ); document.write( "Let $\"+b+\"$ = number of benches
\n" ); document.write( "----------------------------
\n" ); document.write( "The thing they don't mention, but is very
\n" ); document.write( "important is that the 8 students times the
\n" ); document.write( "number of benches they are seated on is
\n" ); document.write( "all of the students.
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+b+=+n%2F8+%2B+3+\"$
\n" ); document.write( "(2) $\"+5b+%2B+12+=+n+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(1) $\"+8b+=+n+%2B+24+\"$
\n" ); document.write( "(1) $\"+8b+-+n+=+24+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+5b+%2B+12+=+n+\"$
\n" ); document.write( "(2) $\"+5b+-+n+=+-12+\"$
\n" ); document.write( "Subtract (2) from (1)
\n" ); document.write( "(1) $\"+8b+-+n+=+24+\"$
\n" ); document.write( "(2) $\"+-5b+%2B+n+=+12+\"$
\n" ); document.write( " $\"+3b+=+36+\"$
\n" ); document.write( " $\"+b+=+12+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+8b+-+n+=+24+\"$
\n" ); document.write( "(1) $\"+8%2A12+-+n+=+24+\"$
\n" ); document.write( "(1) $\"+96+-+n+=+24+\"$
\n" ); document.write( "(1) $\"+n+=+96+-+24+\"$
\n" ); document.write( "(1) $\"+n+=+72+\"$
\n" ); document.write( "-------------
\n" ); document.write( "There are 72 students and 12 benches
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+b+=+n%2F8+%2B+3+\"$
\n" ); document.write( "(1) $\"+b+=+72%2F8+%2B+3+\"$
\n" ); document.write( "(1) $\"+b+=+9+%2B+3+\"$
\n" ); document.write( "(1) $\"+b+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+5b+%2B+12+=+n+\"$
\n" ); document.write( "(2) $\"+5%2A12+%2B+12+=+n+\"$
\n" ); document.write( "(2) $\"+60+%2B+12+=+n+\"$
\n" ); document.write( "(2) $\"+n+=+72+\"$
\n" ); document.write( "OK\r
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