Question 1075728
<pre>
{{{(b+7)/(b+4)=c/9}}}

{{{9(b+7)=c(b+4)}}}

{{{9(b+7)/(b+4)=c}}}

{{{(9b+63)/(b+4)=c}}}

     <u>       9</u>
b + 4)9b + 63
      <u>9b + 36</u>
           27

{{{c=9+27/(b+4)}}}

b+4 can equal any positive or negative divisor of 27.

The divisors of 27 are

1, -1, 3, -3, 9, -9, -27, 27

There are 8 of them, so the answer is 8.

That's because each one when substituted for b+4 produces 
a pair of integers that satisfies {{{(b+7)/(b+4)=c/9}}}

For example, say, when b+4 = -9, b = -13 and substituting
b = -13 into

{{{(b+7)/(b+4)=c/9}}}

gives

{{{(-13+7)/(-13+4)=c/9}}}

{{{(-6)/(-9)=c/9}}}

{{{6/9=c/9}}}

{{{c=6}}}, so the pair (b,c) = (-13,6) is a pair of integers 

that satisfies {{{(-6)/(-9)=c/9}}}.

So the answer is 8.

Edwin</pre>