Question

A restaurant has x number of tables that seat four people and 5 tables which seat two people. The restaurant can seat N number of people. Write a linear equation for N, number of people, in terms of x. Then, solve for x in terms of N and find x when N equals 150.

Answer 1

This requires that you understand what a function is. The restaurant has a limit for how many people can be seated at one time, and we call this: N. The restaurant also has some number of tables that can seat 4 people and a certain number of tables that can seat 2 people (which we already know that there are 5).

Knowing this we can come up with an equation:

N(x) = 4x + 10

Where N(x) is the maximum number of people that can be seated. I use N(x) because the maximum number of people depend on how many tables can seat 4 people which is x. 4x refers to 4 people times x tables to provide the number of people that can be seated at tables with 4 chairs. 10 refers to what we already know about tables with 2 chairs. We know that 5 tables can seat 2 people each: 5 x 2 = 10.

Solving for x:

N = 4x + 10 (subtract 10 from each side)

N - 10 = 4x (divide each side by 4)

N/4 - 10/4 = x

When N = 150

150/4 - 10/4 = x

x = 140/4 = 35

Answer 2

2(3x-2)\y=12