a piece of cloth costs ₹175.if the piece was 4m longer and each metre costs ₹5 less would have reamined unchanged.how long is the piece? please form a equation then try to calculate the roots of x.
(from quadratic equation)
(from quadratic equation)
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Lets assume length of piece = x meter
cost = 175
cost per meter = 175/x
If it was 4 meter longer,
length = (x + 4)
cost per meter = 175/x - 5 = (175 - 5x)/x
total cost = (x + 4) * (175 - 5x)/x = 175
(x + 4)(175 - 5x) = 175x
175x - 5x² + 700 - 20x = 175x
5x² + 20x - 700 = 0
x² + 4x - 140 = 0
x² + 14x - 10x - 140 = 0
x(x + 14) - 10(x + 14) = 0
(x - 10)(x + 14) = 0
x = 10 or -14
length cannot be negative, so x = 10 meter
cost = 175
cost per meter = 175/x
If it was 4 meter longer,
length = (x + 4)
cost per meter = 175/x - 5 = (175 - 5x)/x
total cost = (x + 4) * (175 - 5x)/x = 175
(x + 4)(175 - 5x) = 175x
175x - 5x² + 700 - 20x = 175x
5x² + 20x - 700 = 0
x² + 4x - 140 = 0
x² + 14x - 10x - 140 = 0
x(x + 14) - 10(x + 14) = 0
(x - 10)(x + 14) = 0
x = 10 or -14
length cannot be negative, so x = 10 meter
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Let the length be x
( x+4) ( 175/x - 5) = 175
( x+4) ( 175 - 5x)/ x= 175
CROSS MULTIPLY
175x + 700 -5x^2-20x = 175x
5x^2 +20x -700 = 0
x^2 +4x - 140 = 0
( x-10) ( x+14) = 0
x =10 meters ANSWER
CHECK
175/10 = 17.5 per meter
14 X 12.5 = 175
( x+4) ( 175/x - 5) = 175
( x+4) ( 175 - 5x)/ x= 175
CROSS MULTIPLY
175x + 700 -5x^2-20x = 175x
5x^2 +20x -700 = 0
x^2 +4x - 140 = 0
( x-10) ( x+14) = 0
x =10 meters ANSWER
CHECK
175/10 = 17.5 per meter
14 X 12.5 = 175
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