Question

不完整

1
1.
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

There are 20 tables that seat 4 people and 40 tables that seat 2

people at the restaurant.

Explanation:

Let's break this down. Let
`\( x \)` be the number of tables for 4 people and
`\( y \)` be the number of tables for 2 people.

1. The total number of tables is given as 60:
`\( x + y = 60 \)`.

2. Each table for 4 people seats 4 individuals, and each table for 2 people seats 2 individuals. So, the total number of people seated is given as
`\( 4x + 2y = 160 \)`.

Now, let's solve these simultaneous equations.

From the first equation, we can express
`\( x \)` in terms of
`\( y \): \( x = 60 - y \)`.

Substitute this expression into the second equation:

`\[ 4(60 - y) + 2y = 160 \]`

Simplify and solve for
`\( y \)`:

`\[ 240 - 4y + 2y = 160 \]`

`\[ -2y = -80 \]`

`\[ y = 40 \]`

Now that we know
`\( y \)`, substitute it back into the first equation to find
`\( x \)`:

`\[ x + 40 = 60 \]`

`\[ x = 20 \]`

Therefore, there are 20 tables that seat 4 people
`(\( x \))` and 40 tables that seat 2 people
`(\( y \))` at the restaurant.