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.

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

To write a linear equation in terms of N, we need to determine the total number of seats available in the restaurant.

First, we need to calculate the total number of seats in the tables that seat four people, which is given by 4x (where x represents the number of tables that seat four).

Next, we need to calculate the total number of seats in the tables that seat two people, which is given by 2 * 5 (since there are 5 tables that seat two).

Therefore, the total number of seats in the restaurant is 4x + 2 * 5.

Since N represents the total number of people the restaurant can seat, we can set up the linear equation as follows:

N = 4x + 2 * 5

To solve for x in terms of N, we can rearrange the equation:

4x = N - 2 * 5
4x = N - 10
x = (N - 10) / 4

To find x when N equals 150, plug in N = 150 into the equation:

x = (150 - 10) / 4
x = 140 / 4
x = 35

Therefore, when N equals 150, x equals 35.

2(3x-2)\y=12