SOLUTION: If 3 students sit on each bench then one student will be left. IF 4 students sit on each bench one bench will be left . Find number of students and number of benches in the clas

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If 3 students sit on each bench then one student will be left. IF 4 students sit on each bench one bench will be left . Find number of students and number of benches in the clas      Log On


   

Question 890422: If 3 students sit on each bench then one student will be left. IF 4 students sit on each bench one bench will be left . Find number of students and number of benches in the class.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = the number of benches
Let +s+ = the number of students
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(1) +s+%2F+3+=+b+%2B+1%2F3+
(2) +b+=+s%2F4+%2B+1+
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(1) +s+=+3b+%2B+1+
(2) +4b+=+s+%2B+4++
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(1) +s+-+3b+=+1+
(2) +-s+%2B+4b+=+4+
Add the equations
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+b+=+5+
and
(1) +s+=+3%2A5+%2B+1+
(1) +s+=+16+
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There are 16 students and 5 benches
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check:
( 3 students )x( 5 benches ) = ( 15 students ) + ( 1 extra student )
and
( 16 students ) / ( 4 students per bench ) = ( 5 benches ) - ( 1 extra bench )
Hope this helps