the question is in the descripition

Question

the dance comittee says they now expect double the number of people to attend the dance, for a total of 220 people.you scramble to find larger tables and now will only use the tables that seat 4 people and tables that seat 8 people. brain

a: write an equation that describes the relationship between the quatity of tabels that seat 4 and the quatity of tables that seat 8, assuuming exactly 220 people need seats

B: graph the line for the equation you wrote in part a. label your axis.

c: find both intercepts of the line you graphed in part b

d: what do these quantities represent in this context? do theyh make sense? why or why not?

E: you decide to get 18 tables that seat 8 people. how many tables that seat 4 people will you need to seat 220 people in attendance

compare the equations you wrote in questions 1a and 2a to the graphs you created in questions 1b and 2b. what do you notice? what conlusions, if any, can you make about the solution to both equations?

Answer 1

Establish your variables, Since the question asks for the number of tables that seats 4 and the number of tables that seat 8, your variables need to represent those two cases. I'll say, let "x" represent the number of tables that seat 4 and let "y" be the number of tables that seat 8. So the total number of people sitting at 4-person tables will be 4x and the total number of people sitting at 8-person tables will be 8y and their sum is 220 so:

4x + 8y = 220

There are several ways to graph this but an easy way is to let x = 0 and solve for y:

4(0) + 8(y) = 220

8y = 220

y = 27.5 (realistically, this can't happen since there can't be half a table but it still will create a graph that works)

Then let y = 0 and solve for x:

4x + 8(0) = 220

4x = 220

x = 55

Now, graph the points (0, 27.5) and (55, 0) and connect them with a line. Like this:

You should be able to answer the rest of the questions based on what I've helped you with.