Question

The restaurant La Poutine opens can accommodate 74 guests with its small counter and its 21 tables. The dining room includes tables for 4 people and tables for 2 people. If 8 customers can be at the counter, how many tables are there for 4 people in the restaurant?

Two-way tables
ANSWERED
asked 2021-01-06
The restaurant La Poutine opens can accommodate 74 guests with its small counter and its 21 tables. The dining room includes tables for 4 people and tables for 2 people. If 8 customers can be at the counter, how many tables are there for 4 people in the restaurant?

Answers (1)

2021-01-07
Step 1
There are 21 tables and a small counter in the restaurant that accommodate 74 guests. The tables are of two types: tables for 4 people and tables for 2 people. Assume there are x tables for 4 people and y tables for 2 people. The first equation becomes
x+y=21
Step 2
As there are 8 customers that can be at the counter, the customers occupying tables will become
74-8=66
Step 3
The second equation can be formulated as
4x+2y=66 Step 4
Use elimination method in order to find the value of x and y as follows. \(\begin{cases} x+y=21&\times(-2)\\ 4x+2y=66& \end{cases}\)
\(-2x-2y=-42\)
\(4x+2y=66\)
\(2x=24 \text{On addition}\)
\(x=12\) Step 5 Obtain y as follows. \((12)+y=21 \ \because x=12\)
\(y=21-12\)
\(y=9\) Step 6
Hence, there are 12 tables for four people sitting and 9 tables for two people sitting. Therefore, the number of tables for 4 people in the restaurant is 12.
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