Question

use a system of linear equations to solve the following problem.
a new restaurant is to contain two - seat tables and four - seat tables. fire codes limit the restaurants maximum occupancy to 74 customers. if the owners have hired enough servers to handle 22 tables of customers, how many of each kind of table should they purchase?
they should purchase two - seat tables and four - seat tables.

Explanation:

Step1: Set up variables

Let \(x\) be the number of two - seat tables and \(y\) be the number of four - seat tables.

Step2: Establish equations

The total number of tables: \(x + y=22\) (since there are 22 tables in total).
The total number of customers: \(2x + 4y=74\) (as two - seat tables hold \(2x\) customers and four - seat tables hold \(4y\) customers, and the maximum occupancy is 74).

Step3: Solve the system of equations

From \(x + y=22\), we get \(x = 22 - y\).
Substitute \(x = 22 - y\) into \(2x + 4y=74\):

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Substitute \(y = 15\) into \(x = 22 - y\), we get \(x=22 - 15=7\).

Answer:

They should purchase \(7\) two - seat tables and \(15\) four - seat tables.