I need help with a worded problem algebraic Question

#LionHeart34

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Nov 27, 2019
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Two rectangular plots of land are equal in area .The length of the first plot is one and half times it's width.The length of the second plot is 3 metres less than 15 times it's width.
Denoting the width of the first plot by x metres and the width of the second plot by y metres. Show that:
X^2 - 10y^2 + 2y =0

What I did was to draw the two plots and label them but I am not sure the method I should use to get
X^2 - 10y^2 + 2y =0 and what they mean by denoting the x and y
 
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lev888

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Write expressions showing how lengths depend on corresponding widths. Write expressions for areas. Since areas are the same you get an equation.
 

HallsofIvy

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Two rectangular plots of land are equal in area .The length of the first plot is one and half times it's width[\quote]
Taking the width to be x, the length is "one and a half times" (or 3/2 times) x. The length is 3x/2 so the area is \(\displaystyle (3x/2)(x)= 3x^2/2\)

The length of the second plot is 3 metres less than 15 times it's width.
Taking the width to be y the length is 15y- 3 so the area is \(\displaystyle (15y- 3)y= 15y^2- 3y\).

Denoting the width of the first plot by x metres and the width of the second plot by y metres. Show that:
[/tex]x^2 - 10y^2 + 2y =0[/tex]
.
The two areas are equal so \(\displaystyle 3x^2/2= 15y^2- 3y\). Multiply both sides by two to get rid of that fraction: \(\displaystyle 3x^2= 30y^2- 6y\). Divide both sides by 3 to simplify: \(\displaystyle x^3= 10y^2- 2y\).

What I did was to draw the two plots and label them but I am not sure the method I should use to get
X^2 - 10y^2 + 2y =0 and what they mean by denoting the x and y
It means use the letters, "x" and "y", to represent the numerical values of the two widths. That's the basic concept in algebra.
 
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