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?
A minimum of ___ long-sleeved shirts can be purchased.
A maximum of ___ long-sleeved shirts can be purchased.
A minimum of ___ long-sleeved shirts can be purchased.
A maximum of ___ long-sleeved shirts can be purchased.
2 answers:
Answer:
The highest number of long-sleeved shirts that can be ordered is 8
and
The lowest number of long-sleeved shirts that can be acquired is 0
Step-by-step breakdown:
Let y denote the quantity of short sleeves and x indicate the quantity of long sleeves.
According to the stipulated conditions:
Members of a school club are purchasing coordinating shirts. They understand that a minimum of 25 members will opt for a shirt.
therefore, we have;
or
....[1]
Given that long-sleeved shirts are priced at $10 each and short-sleeved shirts at $5 each.
Thus;
The total expense for long sleeves amounts to 10x and
the total cost of short sleeves is 5yMoreover; the club has a budget that does not exceed $165
therefore;
......[2]
By plotting the inequality functions:
Graphing equations [1] and [2] produces a maximum at the coordinates (8, 17)
thus, x= 8.
Taking the minimum value of x =0 results in y falling between 25 and 33.
consequently, the solution space is situated between the intersecting lines to the left.
In conclusion, a maximum of 8 long-sleeved shirts can be obtained, while the minimum number of long-sleeved shirts that can be bought is 0
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