Question 97772: Hi! can you please help me solve this problem out??
It goes...
Al's flower garden measures 25 feet by 35 feet. He has enough crushed stone to cover 325 square feet. If he uses the stone to build a path around his garden, what is the maximum possible width of the path?
Answer by mathslover(157)   (Show Source):
You can put this solution on YOUR website! Let x be the maximum possible width of the path
length of the garden including the path = 35 + 2x ( 2x because x for each side)
width of the garden = 25 + 2x
total area of the garden with the path = (35+2x)(25+2x)
also area of the garden without the path= 35* 25
area of the path = (35+2x)(25+2x) - 35*25
Now the area should be less than or equal to 325 sq feet because that is the amount of crushed gravel Al has got.
For maximum path, area of the path = 325
=> (35+2x)(25+2x) - 35*25 =325
32*25 + 70x + 50x +4x^2 -35*25 = 325
4x^2 + 120x - 325=0
4x^2 + 130x -10x -325=0
2x(2x+65) - 5(2x+65)=0
(2x+65)(2x-5)=0
x=5/2 ignoring the negative -65/2
Maximum width of the path of 2.5m
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