Question

A restaurant has 23 tables. Some of the tables seat 4 persons and the rest seat two persons. In all, 76 persons can be seated at once. How many tables of each kind are there?

Answer 1

15 tables with 4 seats and 8 tables with 2 seats.

Explanation:

x = 4 seated tables

y = 2 seated tables

x + y = 23

4x + 2y = 76

Multiply first equation by -2 to cancel y's:

-2x - 2y = -46

4x + 2y = 76

2x = 30

x = 30 / 2

x = 15

And we said 23 tables so:

23 - 15 = 8

x = 15

y = 8