Question 1098759: The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have P = 2L + 2W
P > 62, therefore 2L + 2W > 62
you have W <= L - 10
your system of inequalities would be:
2L + 2W > 62
W <= L - 10
x >= 0
y >= 0
you can take any perimeter > 62 and solve for L and W as follows:
for example:
P = 100
2L + 2W = 100
W = L-10, therefore 2L + 2L - 20 = 100
4L = 120
L = 30
W = 20
2*30 + 2*20 = 60 + 40 = 100
since W <= L - 10, then W can be anything less than or equal to 20 which means that L can be anything greater than 30.
W, however, can't be greater than 20 if P = 100, because W would then not be at least 10 less than L.
example 1:
W = 10
2L + 2W = 100
2L + 20 = 100
2L = 80
L = 40
2*40 + 2*10 = 80 + 20 = 100
this is ok since W is at least 10 less than L.
example 2:
W = 21
2L + 2W = 100
2L + 42 = 100
2L = 58
L = 29
2L + 2W = 58 + 42 = 100
this is not ok since W is not at least 10 less than L.
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