SOLUTION: A shop has some pigeons and some cages. If the shopkeeper tries to put 5 pigeons in each cage, then there will be 1 cage left. If the shopkeeper tries to put 3 pigeons in each cage

Algebra ->  Equations -> SOLUTION: A shop has some pigeons and some cages. If the shopkeeper tries to put 5 pigeons in each cage, then there will be 1 cage left. If the shopkeeper tries to put 3 pigeons in each cage      Log On


   

Question 1129547: A shop has some pigeons and some cages. If the shopkeeper tries to put 5 pigeons in each cage, then there will be 1 cage left. If the shopkeeper tries to put 3 pigeons in each cage, there will be 1 pigeon left. How many pigeons and cages are there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = number of pigeons
Let +c+ = number of cages
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(1) +5%2A%28+c-1+%29+=+p+
(2) +3c++=+p+-+1+
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(1) +5c+-+5+=+p+
(1) +5c+-+p+=+5+
and
(2) +-3c+%2B+p+=+1+
---------------------------
Add the equations
+2c+=+6+
+c+=+3+
and
(2) +3%2A3+=+p+-+1+
(2) +p+=+10+
There are 10 pigeons and 3 cages
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check:
5 pigeons in each cage is +2%2A5+=+10+ pigeons
and there is 1 cage left
3 pigeons in each cage is +3%2A3+=+9+ and 1
pigeon left makes 10 pigeons
OK