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Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10 each and short-sleeved shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeved shirts that can be purchased?

User Adetunji
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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.

User Matthew Goulart
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