The owners of River View Bakery have hired enough servers to handle 17 tables of customers, and the fire marshal has approved the restaurant for a limit of 56 customers. The owners need to purchase two-seat and four-seat tables to accommodate the customers.
1. Write a system of equations to illustrate the situation. Use x for the two-seat tables and y for the four-seat tables.
X=6
Y=11
2x + 4y = 56
x + y = 17 ---- x = -y + 17
substitute
2(-y + 17) + 4y = 56
-2y + 34 + 4y = 56
2y + 34 = 56
2y = 22
y = 11
2x + 4(11) = 56
2x + 44 = 56
2x = 12
x = 6
Sure, here's the system of equations to illustrate the situation:
Equation 1: x + y = 17 (This equation represents the number of tables)
Equation 2: 2x + 4y = 56 (This equation represents the total number of customers that can be accommodated)
To write a system of equations for this situation, let's first define the variables:
x = number of two-seat tables
y = number of four-seat tables
Now, let's establish the constraints:
1. The total number of tables cannot exceed 17:
x + y ≤ 17
2. The total number of customers cannot exceed 56:
2x + 4y ≤ 56
Therefore, the system of equations is:
x + y = 17
2x + 4y = 56
These equations represent the constraints on the number of tables and customers that the owners of River View Bakery have to consider.
x = 2-seat tables
y = 4-seat tables
2x + 4y = 56 (max)
x + y = 17
Solve for x and y that allows the maximum number of customers
2x + 2y = 34
2y = 22
y = 11
x = 6