Good point. Have a look what you can do with bc. I moved everything inside the string passed to bc:
echo 'scale=0;a=800;b=700;c=.15;print "\na=",a,"\nb=",b,"\nc=",c,"\n";if (a < b*(c+1)) print "true\n" else print "false\n"' | bc
Move the comparison in bc since the results are floating point numbers.
Code:
echo "($b*$c+$b) <= $a" | bc
0
echo "($b*$c+$b) >= $a" | bc
1
To test for equality, you need to compare the difference to a small value. This allows for rounding errors.