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.

Question

1. Write a system of equations to illustrate the situation. Use x for the two-seat tables and y for the four-seat tables.

Answer 1

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

Answer 2

X=6

Y=11

Answer 3

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