Question 1020786: How many pairs of integers (b,c) satisfy the equation (b+7)/(b+4)=c/9?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! The equation 
is equivalent to 
==>  , after transposing 1 to the right side;
==>  , after combining terms,
==> 27 = (b+4)(c-9), after cross multiplying.
Since both b+4 and c - 9 are supposed to be integers, there are eight possibilities
(i) b+4 = 1, c-9 = 27 ==> b = -3, c=36
(ii) b+4 = 3, c-9 = 9 ==> b = -1, c = 18
(iii) b+4 = 9, c-9 = 3 ==> b = 5, c = 12
(iv) b+4 = 27, c-9 = 1 ==> b = 23, c = 10
(v) b+4 = -1, c-9 = -27 ==> b = -5, c = -18
(vi) b+4 = -3, c-9 = -9 ==> b = -7, c = 0
(vii) b+4 = -9, c-9 = -3 ==> b = -13, c = 6
(viii) b+4 = -27, c-9 = -1 ==> b = -31, c = 8
Therefore there are 8 pairs of integers that will satisfy the original equation.
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