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
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?

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.