We have a number of birds and we bought cages to put them in. If we put $7$ birds in each cage then one bird is left over. If we put $9$ birds in each cage then one cage is left over. Find the number of birds and cages.
Any ideas or hints?
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$5$? aM I wrong? – Paris Lamp Nov 23 '15 at 14:40
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1The modulo solution is too complicated and incorrect?! It would suggest that C = 12 is also a solution. Just $7C + 1 = 9(C-1)$ already gives $C = 5$. – Pieter21 Nov 23 '15 at 14:51
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we have 2 solutions? – Paris Lamp Nov 23 '15 at 15:00
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Let $x$ = number of cages. Then $7x+1=9(x-1)$ so $x=5$ cages is correct, as you commented. – Marconius Nov 23 '15 at 18:03
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Also $1$ bird and $100000$ cages is formally correct... – Crostul Nov 23 '15 at 20:23
1 Answers
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If $B$ is the number of birds, and $C$ is the number of cages, we have the following: $$9(C-1) = B\ ;\ \ 7C + 1 = B$$ You can quickly reduce this to find that $\dots$
jameselmore
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