Notice that 143 is close to 15*10=150
There are no 150 guests, so the tables cannot all have 10 people.
We try 9. If there are 9 people at each of the 15 tables there are
15*9=(10+5)*9=10*9+5*9=90+45=135 people
there are still 143-135=8 people left, which can be sited in 8 of the tables.
So we have 8 tables of 10 people and 7 tables of 9 people.
Answer: 9