directions=determine the best method to solve each system of equations. then solve the system

Question=the owners of the river view restaurant have hired enough servers to handle 17 tables of costumers, and the fire marshal has approved the restaurant for a limit of 56 customers. How many two-seat tables and how many four-seat tables should the owners purchase

Question

directions=determine the best method to solve each system of equations. then solve the system 

Question=the owners of the river view restaurant have hired enough servers to handle 17 tables of costumers, and the fire marshal has approved the restaurant for a limit of 56 customers. How many two-seat tables and how many four-seat tables should the owners purchase

anonymous · Answer

So can you come up with a system of equations first of all?

anonymous · Answer

The first step is to come up with some variables.

anonymous · Answer

how do u do that

anonymous · Answer

"the owners of the river view restaurant have hired enough servers to handle 17 tables of costumers"

When you read this, you should think, we need a variable for tables and a variable for customers.

anonymous · Answer

So we'll say the number of tables is $t$ and the number of customers is $c$.

Does that make sense so far?

anonymous · Answer

yea

anonymous · Answer

so what would that part of the equation look like

anonymous · Answer

"the owners of the river view restaurant have hired enough servers to handle 17 tables of costumers, and the fire marshal has approved the restaurant for a limit of 56 customers."

This can be written as:$$
t\le 17\quad c\le 56
$$

anonymous · Answer

"How many two-seat tables and how many four-seat tables should the owners purchase"

Okay now we need a variable for these...

anonymous · Answer

the answer has to be in the form of the points on a graph
and it ether has to be subtraction substitution addition or multiplication

anonymous · Answer

We can let $x$ be two-seat tables.  We can let $y$ be four-seat tables.

anonymous · Answer

We know that $$
x+y = t
$$The number of tables is equal to the total of two-seat and four-seat tables.
We also know: $$
2x+4y=c
$$The number of customers is  2 for each two-seat and 4 for each four-seat.

anonymous · Answer

Does this make sense?

anonymous · Answer

yea

anonymous · Answer

Well simplify things a bit, and our final system will be: $$
x+y=17\
2x+4y=52
$$

anonymous · Answer

So we have a system, we just need to solve for it.  Which method do you think is best?

anonymous · Answer

subtraction
and it would be 2x+4y=56 because there can be 56 customers

anonymous · Answer

Oh, ok.

anonymous · Answer

Are we done then?

anonymous · Answer

yea thank you