Let x = the number of white collar workers
"total number of employees is 117" means
(white collar workers) + (blue collar workers) = 117
(white collar workers) + (blue collar workers) = 117
(blue collar workers) = 117 - x
"five more than seven times more blue color workers than white color workers" means
5 + 7 * (white collar workers) = (blue collar workers)
5 + 7x = 117 - x
8x = 112
x = 14
There are 13 white collar workers.
(blue collar workers) = 117 - x = 117 - 14 = 103
There are 103 blue collar workers.
Check: Is 5 + 7(14) = 103 ?
5 + 98 = 103 ?
103 = 103 ?yes