Question

A dining hall had a total of 25 tables - some long rectangular tables and some round ones. Long tables can seat 8 people. Round tables can seat 6 people. on a Busy evening, all 190 seats at the tables are occupied. How many long tables, x, and how many round tables, y, are there?

Answer 1

There are 20 long tables and 5 round tables y.

Explanation:

Given:

long tables x + round tables y = total of 25 tables

8seats ·x +6seats ·y = 190 seats

Find x and y:

x+y= 25 so x= 25-y

8x+6y = 190, we substitute x for 25-y to find y

8(25-y) +6y = 190, we distribute 8 in parenthesis

200 -8y+6y = 190, combine like terms

200 -2y = 190, subtract 200 from both sides

-2y = 190-200, combine like terms

-2y = -10, divide both sides by -2

y = 5

x+y = 25, substitute y for 5

x+5 = 25, subtract 5 from both sides

x= 20

Conclusion:

There are 20 long tables and 5 round tables y.

Check :

20·8+5·6 = 160+30 = 190 seats