What is the fraction of blue beads?

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A tin contains red, white and blue beads in the ratio red:white:blue = x:2x:x^2

First we should find the total number of beads in the tin:

x + 2x + x^2 = 3x + x^2

The number of blue beads is x^2

So the fraction of blue beads, is (number of blue beads)/(total number of beads in the tin)

ie (x^2)/(3x+x^2)

we can simplify this further by taking an x out:

x(x)/x(3+x), so an x from the top and bottom cancels out, leaving us with:

x/(x+3)

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