Using elimination, write and solve an equation for the following word problem: The owners of the Riverview Restaurant have hired enough servers to handle 17 tables of customers, and the fire marshal has approved the building for a limit of 56 customers. How many two-seat tables and four-seat tables should the owners purchase?

Question

anonymous · Answer

Given the assumption that the restaurant wants to maximize seating, you want to use the most number of 4-seat tables.
Max customers = 56
max tables = 17
2x + 4y = 56
I'd set 4y = 56 and solve getting y = 14. This would maximize tables and leave 3 extra servers that otherwise would be working 2 customer tables that are less profitable.
So the restaurant should purchase 0 2 seat tables and 14 4 seat tables unless you are required to purchase 17 tables. In which case i'll analyze it further if you want

radar · Answer

Problem states to solve using elimination.
Let x = number of two seat tables.
Let y = number of 4 seat tables
EQUATION 1.  x+y = 17 Tables (Given)
Now lets form the equation for the total people which is allowed to be 56.
2x +4y = 56 (two per x, the number of 2 seat tables and 4 per y the 4 seat tables.
x + y = 17   (Equation 1 from above) 
x  + 2y = 28   This is the people equation divided through by 2  subtract to eliminate.
0    -y= -11, then y the 4 seater tables is 11, the two seater tables would then
be 17-11=6.
Follow it.  Check it.