Question

a restaurant has a total of 60 tables some of the tables can seat 4 people and some can seat 2 people all of the seats are occupied when there are 160 people seated how many tables for 4 are there

Answer 1

Answer: There are 10 tables for 4 people in the restaurant.

Explanation:

1. Assign variables: Let x be the number of tables that seat 4 people, and y be the number of tables that seat 2 people.

2. Write equations: We know that the restaurant has a total of 60 tables, so x + y = 60. We also know that all seats are occupied when there are 160 people seated, so 4x + 2y = 160.

3. Solve the system of equations: We can use the first equation to solve for y: y = 60 - x. We can substitute this expression for y in the second equation to get: 4x + 2(60 - x) = 160. Simplifying this equation gives us: 2x + 60 = 80. Solving for x gives us: x = 10.

4. Interpret the solution: There are 10 tables that seat 4 people in the restaurant. We can find the number of tables that seat 2 people by using the equation we found for y: y = 60 - x. Substituting x = 10 gives us y = 50. Therefore, there are 50 tables that seat 2 people in the restaurant.

Answer 2

This question is based on the concept of linear equation. Therefore, the equation would be, 10x+20y=160 or 25x+10y=160 to represent the situation.

Given:

He wants to have only tables for 4 and tables for 6. The total number of tables is 160.

And x represent the number of 4 seat tables and y represent the number of 6 seat tables.

We need to determined an equation to represent the situation.

Let x represent the number of 4 seat tables and y represent the number of 6 seat tables.

According to the question,

There are different combinations we can make as below,

For example :

10 tables of 4 and 20 tables of 6

or

25 tables of 4 and 10 tables of 6

Therefore, the equation would be, 10x+20y=160 or 25x+10y=160 to represent the situation.