2)Banquet Seating A banquet hall offers two types of tables for rent: 6-person rectangular tables at a cost of $26 each and 10-person round tables at a cost of $51 each. Kathleen would like to rent the hall for a wedding banquet and needs tables for 250 people. The room can have a maximum of 35 tables and the hall only has 15 rectangular tables available. How many of each type of table should be rented to minimize cost and what is the minimum cost?

The number of rectangular tables =

The number of round tables =

The minimum cost =

To find the minimum cost and how many of each table type should be rented, we can set up a system of equations.

Let's assume x represents the number of rectangular tables and y represents the number of round tables.

1) The total number of tables needed is given by the equation:
x + y = 35

2) The total number of people the tables can accommodate is given by the equation:
6x + 10y = 250

Now, we can solve these equations to find the values of x, y, and the minimum cost.

To solve the system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution:

From equation 1, we can express x in terms of y:
x = 35 - y

Substituting this value of x in equation 2, we get:
6(35 - y) + 10y = 250

Simplifying the equation:
210 - 6y + 10y = 250

Combining like terms:
4y = 40

Dividing both sides by 4:
y = 10

Substituting the value of y back into equation 1, we can find x:
x + 10 = 35
x = 25

So, the number of rectangular tables is 25 and the number of round tables is 10.

To find the minimum cost, we can calculate the total cost of renting these tables:

Cost of rectangular tables = 25 * $26 = $650
Cost of round tables = 10 * $51 = $510

Total cost = $650 + $510 = $1160

Therefore, the minimum cost for renting the tables is $1160.

168