Circular and rectangular tables are set up for a banquet. There are 9 tables set up with 80 chairs. Each circular table has 8 chairs and each rectangular table has 10 chairs. How many tables of each type have been set up? Write and solve a linear system of equations by graphin
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the number of circular tables is C, and the number of rectangular tables is R. We can write two equations based on the number of chairs:
1) The total number of chairs: 8C + 10R = 80
2) The total number of tables: C + R = 9
Now, we can solve the system of equations by graphing:
1) Equation 1: 8C + 10R = 80
Rearrange the equation to slope-intercept form:
10R = 80 - 8C
R = (80 - 8C) / 10
R = 8 - (4/5)C
2) Equation 2: C + R = 9
Rearrange the equation to slope-intercept form:
R = 9 - C
To graph these equations, we can assign the values of C as the x-values and solve for R (using the equations we derived). We can then plot the points on the graph.
Here's a table to help:
C | R
--------------
0 | 9
1 | 8
2 | 7
3 | 6
4 | 5
5 | 4
6 | 3
7 | 2
8 | 1
9 | 0
Now let's plot these points on the graph:
9 | x
8 | x
7 | x
6 | x
5 | x
4 | x
3 | x
2 | x
1 | x
0 |_______________________________________
0 1 2 3 4 5 6 7 8 9
The graph will show a line connecting the plotted points. The intersection point of the two lines represents the solution to the system of equations.
Based on the graph, it appears that there are 6 circular tables and 3 rectangular tables set up for the banquet.