Bunuel wrote:
The sides of rectangle A are each multiplied by x to form rectangle B and by y to form rectangle C. When multiplied by x, the area of rectangle A equals 10, and when multiplied by y, the area of rectangle A equals 5. If the difference in area between rectangle B and C is 300, what is x−y?
A. 5
B. 20
C. 30
D. 50
E. 60
Length = \(l\), Width = \(w\).
Area of rectangle A = \(lw\).
Area of rectangle B = \(lx*wx = (x^2)lw\).
Area of rectangle C = \(ly*wy = (y^2)lw\).
\(lwx = 10, lwy = 5\).
\(x = \frac{10}{(lw)}, y = \frac{5}{(lw)}\)
\(lw(x-y) = 10-5 = 5\).
\(lw(x^2-y^2) = 300\)
\(lw(x+y)(x-y) = 300\)
\(5(x+y) = 300\)
\((x+y) = 60\).
\(\frac{10}{(lw)} + \frac{5}{(lw)} = 60\)
\(15lw = 60(lw)^2\)
\(lw = \frac{15}{60} = \frac{1}{4}.\)
\((x-y) = 5*4 = 20\).