Question

The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of 12 tables and 25 booths, which will seat a total of 310 people. The second plan consists of 11 tables and 23 booths, which will seat a total of 285 people. How many people can be seated at each type of table?

Answer 1

Answer: Each table can seat 5 people and each booth can seat 10 people.

Explanation:

According to the first plan, there are 12 tables and 25 booths, and the total number of people seated is 310. This can be written as:

12x + 25y = 310

According to the second plan, there are 11 tables and 23 booths, and the total number of people seated is 285. This can be written as:

11x + 23y = 285

Multiplying the first equation by 11 and the second equation by 12, we get:

132x + 275y = 3410

132x + 276y = 3420

Subtracting the second equation from the first equation, we eliminate 'x':

275y - 276y = 3410 - 3420

-y = -10

Dividing both sides of the equation by -1, we get:

y = 10

'

Substituting this value of 'y' into the first equation, we can solve for 'x':

12x + 25(10) = 310

12x + 250 = 310

12x = 310 - 250

12x = 60

x = 60/12

x = 5

Therefore, each table can seat 5 people, and each booth can seat 10 people.

Answer 2

Answer: In the first plan, each table can seat 5 people, and each booth can seat 10 people.

Explanation:

For the first plan:

12T + 25B = 310

For the second plan:

11T + 23B = 285

Now, you can solve this system of equations to find the values of T and B. There are various methods to solve systems of equations; one common method is substitution or elimination.

Let's use the elimination method:

Multiply the first equation by 23 and the second equation by 25 so that the coefficients of B will cancel each other when the equations are added.

276T + 575B = 7130

275T +575B = 7125

Now subtract the second equation from the first:

(276T+575B) − (275T+575B) = 7130 − 7125

This simplifies to:

T=5

Now that you know T=5, you can substitute this value back into one of the original equations to solve for B. Let's use the first equation:

12T+25B=310

12(5) + 25B =310

Solving for B:

60 + 25B = 310

25B = 250

B=10

So, in the first plan, each table can seat 5 people, and each booth can seat 10 people.

You can follow a similar process for the second plan to find the number of people each table and each booth can seat.