Question 158976
Hi, Hope I can help
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The length of a rectangular playing field is 5 meters less than twice its width. if 230 meters of fencing goes around the field, find the dimensions of the field.
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First we have to find variables for length and width
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The length of a rectangular playing field is 5 meters less than twice its width.
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We can name the width "x"
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The length of a rectangular playing field is 5 meters less than twice its width, if the width is "x", and the length is 5 meters less than twice the width, this is how you right the length, {{{ 2(width) - 5 }}}, width = "x" {{{ 2(x) - 5 }}} = {{{ 2x - 5 }}}
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The length = {{{ 2x - 5 }}}
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The width = {{{ x }}}
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Since 230 meters of fencing goes around the field, we are trying to find the Perimeter of the field
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The length = {{{ 2x - 5 }}}
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The width = {{{ x }}}
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The Perimeter of a Rectangle is = {{{ 2(width) + 2(length) = Perimeter }}}
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They give us the Perimeter, 230 meters, so we can replace "Perimeter" with "230"
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{{{ 2(width) + 2(length) = Perimeter }}} = {{{ 2(width) + 2(length) = 230 }}}
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Since the width = {{{ x }}}, and the length = {{{ 2x - 5 }}}, we can replace "width" and "length" with our variables
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{{{ 2(width) + 2(length) = 230 }}} = {{{ 2(x) + 2(2x - 5) = 230 }}}, now just solve for "x"
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We will get rid of the parentheses, and use distribution
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{{{ 2(x) + 2(2x - 5) = 230 }}} = {{{ 2x + highlight(2)(highlight(2x) - 5) = 230 }}} = {{{ 2x + highlight(2)(2x - highlight (5)) = 230 }}} = {{{ 2x + 4x - 10 = 230 }}} (Since the "5" is negative the number will be negative)
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Add like terms
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{{{ 2x + 4x - 10 = 230 }}} = {{{ highlight(2x) + highlight(4x) - 10 = 230 }}} = {{{ 6x - 10 = 230 }}}
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We will move (-10) to the right side
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{{{ 6x - 10 = 230 }}} = {{{ 6x - 10+10 = 230+10 }}} = {{{ 6x = 240 }}}, To solve "x" we will divide each side by "6"
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{{{ 6x = 240 }}} = {{{ 6x/6 = 240/6 }}} = {{{ x = 240 }}} = {{{ x = 40 }}}
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x = "40", we can check by replacing "x" with "40" in our equation
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{{{ 2(x) + 2(2x - 5) = 230 }}} = {{{ 2(40) + 2(2(40) - 5) = 230 }}} = {{{ 80 + 2(80 - 5) = 230 }}} = {{{ 80 + 2(75) = 230 }}} = {{{ 80 + 150 = 230 }}} = {{{ 230 = 230 }}} ( True )
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x = "40"
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Our width and length in variable form were:(Just replace "x" with "40" in our equations)
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The length = {{{ 2x - 5 }}} = {{{ 2(40)-5 }}} = {{{ 80 - 5 }}} = 75
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The width = {{{ x }}} =  40 
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Since the unit is the meter, our answers would be 
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The Length =  75  meters
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The Width =  40 meters
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Hope I helped, Levi