Answer:
Assume "x" represents the number of long-sleeved shirts and "y" represents the number of short-sleeved shirts.
According to the information provided, at least 25 members will receive a shirt. As a result, we may express the equation as:
x + y 25...........(1)
In addition, the club's budget cannot exceed $165. Each long-sleeved shirt costs $10, while each short-sleeved shirt costs $5. As a result, the total cost is stated as:
10x + 5y 165...........(2)
The minimum and maximum quantity of long-sleeved shirts that can be purchased must be determined.
To determine the bare minimum of long-sleeved shirts, we may assume that each of the 25 members will receive a short-sleeved shirt. As a result, equation (1) becomes: x + 25 25 x 0
As a result, the bare minimum of long-sleeved shirts that can be purchased is 0.
To determine the maximum number of long-sleeved shirts, we must solve equations (1) and (2) concurrently. We may do this by using the replacement approach.
We may deduce from equation (1): y ≥ 25 - x
When we substitute this number for "y" in equation (2), we get:
10x + 5(25 - x) ≤ 165
When we simplify this equation, we get:
5x ≤ 40
x ≤ 8
As a result, the total number of long-sleeved shirts that can be ordered is eight.
As a result, the lowest number of long-sleeved shirts available for purchase is 0 and the maximum number of long-sleeved shirts available for purchase is 8.