9 workers
7 workers can make 210 pairs of cup in 6 days, so:
1 worker can make 30 pairs of cup in 6 days, so:
1 worker can make 5 pairs of cup in 1 day.
Using this info, because
the workers need to make 450 pairs of cup in 10 days,
they need to make 45 pairs of cup in 1 day,
each worker can make 5 pairs of cup in 1 day,
so 45/5 = 9 workers
voila!