Question

If Y% of (Y + X) = X% of (X + Y), then find X is what percent of (X + Y)?

Answer 1

x will be 42 percent

Step-by-step explanation:

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Answer 2

STEP BY STEP EXPLANATION

(x/100)x + (y/100)y = 0.02(xy)

(x^2)/100 + (y^2)/100 = 0.02(xy)

Multiply both sides by 100,

x^2 + y^2 = 50xy

x^2 - 50xy + y^2 = 0

Complete the squares.

(x^2 - 50xy + 25y^2) - 24y^2 = 0

(x - 5y)^2 - 24y^2 = 0

This is a difference of squares.

(x - 5y + (sqrt (24))y)(x - 5y - (sqrt(24))y) = 0

x - 5y + (sqrt (24))y) = 0 or x - 5y - (sqrt(24))y = 0

x = 5y +/- (sqrt(24)y) = y (5 + / - (sqrt(24))

y as a percentage of x is expressed as y/x*100.

x/y = 5 +/- (sqrt(24)) = 9.89898 or 0.10102

y/x = 0.10102 or 9.89902

(y/x) * 100 = 10.102 or 989.902

So y is either 10.102% of x or 989.902% of x