A furniture company displays bedroom sets which require 21 square meters of space and living room sets which require 42 square meters of space. The company, which has 546 square meters of available space, wants to display at lease 6 bedroom sets and atleast 5 living room sets. Let x represent the number of bedroom sets and y reperesent the number of living room sets. Write a system of inequalities to represent the number of furniture sets that can be displayed.
21x+42y<=546
x+y>=6
To write a system of inequalities to represent the number of furniture sets that can be displayed, we need to consider the space requirements for each type of furniture set.
Let's start with the bedroom sets. We know that each bedroom set requires 21 square meters of space. If we want to display x bedroom sets, the total space required for the bedroom sets would be 21x square meters. Since we want to display at least 6 bedroom sets, we can write the following inequality:
21x ≥ 21 * 6
Simplifying the right side:
21x ≥ 126
Next, let's consider the living room sets. Each living room set requires 42 square meters of space. If we want to display y living room sets, the total space required for the living room sets would be 42y square meters. Since we want to display at least 5 living room sets, we can write the following inequality:
42y ≥ 42 * 5
Simplifying the right side:
42y ≥ 210
Finally, we need to consider the total available space. The company has 546 square meters of available space, so the total space used by the furniture sets must be less than or equal to 546 square meters. We can write this inequality as:
21x + 42y ≤ 546
So, the complete system of inequalities to represent the number of furniture sets that can be displayed is:
21x ≥ 126
42y ≥ 210
21x + 42y ≤ 546