Question

1. 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?

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Answer 1

x = 20 long tables

y = 5 round table

Explanation:

We have the following system of equations:

x + y = 25

8x + 6y = 190

From the first equation we have:

x = 25 - y

And we replace x in the second equation:

8(25 - y) + 6y = 190

200 - 8y + 6y = 190

200 - 2y = 190

200 - 190 = 2y

10 = 2y

y = 5

Now we insert the value of y in the next equation:

x = 25 - y

x = 25 - 5

x = 20

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