SOLUTION: A piece of cloth costs 200 us. if the price was 5 meter longer, and the cost of each meter of cloth was 2 us less, the cost of the piece would have remained unchanged. how long is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A piece of cloth costs 200 us. if the price was 5 meter longer, and the cost of each meter of cloth was 2 us less, the cost of the piece would have remained unchanged. how long is      Log On


   

Question 550155: A piece of cloth costs 200 us. if the price was 5 meter longer, and the cost of each meter of cloth was 2 us less, the cost of the piece would have remained unchanged. how long is the piece and what is its original price per meter?
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the original length in meters
+200%2Fx+ = original cost/meter
+200+%2F+x+-+2+ = the new cost/meter
+%28+x+%2B+5+%29%2A%28+200%2Fx+-+2+%29+=+200+ us
+200+%2B+1000%2Fx+-+2x+-+10+=+200+
Subtract 200 from both sides
+1000%2Fx+=+2x+%2B+10+
Multiply both sides by x
+1000+=+2x%5E2+%2B+10x+
+x%5E2+%2B+5x+-+500+=+0+
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-500+
+x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-500%29+%29%29%2F%282%2A1%29+
+x+=+%28-5+%2B-+sqrt%28+25+%2B+2000+%29%29+%2F+2+
+x+=+%28-5+%2B-+sqrt%28+2025+%29%29+%2F+2+
+x+=+%28-5+%2B+45%29+%2F+2+ ( can't use the (-) square root )
+x+=+20+
The piece is 20 m long
+200%2Fx+=+200%2F20+
+200%2Fx+=+10+
The original price/m is 10 us
check answers:
+%28+x+%2B+5+%29%2A%28+200%2Fx+-+2+%29+=+200+
+%28+20+%2B+5+%29%2A%28+200%2F20+-+2+%29+=+200+
+25%2A%28+10+-+2+%29+=+200+
+25%2A8+=+200+
+200+=+200+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A piece of cloth costs 200 us. if the cloth was 5 meter longer, and the cost of each meter of cloth was 2 us less, the cost of the piece would have remained unchanged. how long is the piece and what is its original price per meter?
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Let original length of cloth be x meters.
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Original cost per meter = 200/x us
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New length of cloth = x+5 meters
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New cost per meter: [200/(x+5) - 2] us
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New cost of the cloth = [200/(x+5) - 2]*(x+5) = 200
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Equation:
[200/(x+5) - 2]*(x+5) = 200
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200 - 2(x+5)^2 = 200(x+5)
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100 - (x+5)^2 = 2x+10
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100-[x^2+10x+25] = 2x+10
100-x^2-10x-25 = 2x+10
x^2+12x-65 = 0
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x = [-12 +- sqrt(144-4*-65)]/2
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Positive solution:
x = 4.05
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Original price per meter = 200/x = $49.38
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Cheers,
Stan H.