SOLUTION: Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeve shirts are $10 each and short-sleeve shirts are $5 each. The club c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeve shirts are $10 each and short-sleeve shirts are $5 each. The club c      Log On


   

Question 1030119: Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeve shirts are $10 each and short-sleeve shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeve shirts that can be purchased?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +y+ = number of short sleeve shirts they can buy
Let +x+ = number of long sleeve shirts they can buy
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+5y+%2B+10x+%3C=+165+
+y+%2B+x+%3E=+25+
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+5y+%3C=+-10x+%2B+165+
+y+%3C=+-2x+%2B+33+
and
+y+%3E=+-x+%2B+25+
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Here are the plots:
+graph%28+600%2C+400%2C+-5%2C+20%2C+-10%2C+50%2C+-2x+%2B+33%2C+-x+%2B+25+%29+
From the plot, it looks like ( 8, 17 ) is the maximum point
so, +x+=+8+ is the maximum
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I can go down to +x=0+, and +y+
can be between +y+=+25+ and +y+=+33+
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The solution area is between the lines to the left
of where the lines intersect.
The maximum number of long
sleeve shirts they can buy is 8
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The minimum number of long
sleeve shirts they can buy is 0
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Hope this helps