Question

Lesson 9.1 Sample CR Task 3

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.
10
●
Create and use a model that can be used to determine the number of round and rectangular tables they
set up for the banquet.
● Define your variables.
How many tables of each type have been set up?
Show all work or explain how you determined your solution.
Enter your equation(s), definition of variables, work, and solutions in the box provided.

Answer 1

Using a system of equations where x is the number of circular tables and y is the number of rectangular tables, we found that there are 5 circular tables and 4 rectangular tables at the banquet.

Step-by-step explanation:

To determine the number of round and rectangular tables set up for the banquet, we need to establish a system of equations based on the information given. First, we define our variables: let x be the number of circular tables and y be the number of rectangular tables. The problem states that each circular table has 8 chairs and each rectangular table has 10 chairs. There are a total of 9 tables and 80 chairs.

This information gives us two equations based on the counts of tables and chairs:

1. x + y = 9 (the total number of tables)
2. 8x + 10y = 80 (the total number of chairs)

To solve this system, we can use either substitution or elimination. In this case, we can easily use substitution since the first equation provides a direct relationship between x and y.

We solve the first equation for y: y = 9 - x. Then, we substitute this into the second equation:
8x + 10(9 - x) = 80
8x + 90 - 10x = 80
-2x = -10
x = 5.

Since x is 5, we can find y by substituting x back into the first equation: y = 9 - 5, which gives y = 4.

Therefore, there are 5 circular tables and 4 rectangular tables set up for the banquet.