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.

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.