Question

A party is thrown where 25 tables are used. Each table either sits 4people or 6 people. A total of 116 people can be sat at the tables.

1- if f represent the number of four person tables and s represents the number of six person tables, write a system of equations that models this equation.
2- how many six person tables are there?

Answer 1

Okay, so I'm gonna do this in terms of x and y, because that's what I'm used to.
s= x = 4-person tables
a= y = 6-person tables
x + y = 25
~ You use 25 tables so no matter how many of each kind are there, you end up with 25 tables so it should add up to 25.
4x + 6y = 116
~ You know that there will always be a total of 116 people at the tables. And in this case 4 and 6 are the number of people that can be seated at these tables, so in terms of people, you would say 4x and 6y.
To find out the amount of six people tables, solve for y and that's your answer.
You could do this a variety of ways.
One way is the substitution, for that you would rearrange the first equation for y, then plug in that value for y in the second equation and then solve for y. That value you get is your answer.