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 Originally Posted by spoonitnow
So now we have a big ass equation of one variable, 0 = 30x + (1/3)(1-x)(-20) + (2/3)(1-x)(43/47)(-20) + (2/3)(1-x)(4/47)(3/4)(50) + (2/3)(1-x)(4/47)(1/4)(3/4)(110) + (2/3)(1-x)(4/47)(1/4)(1/4)(260). I plug that into something like the equation solver at Algebra Simplifier and Math Solver and get x = 0.328, though you're welcome to do it by hand if you want. So Villain has to fold about 32.8% of the time.
I got bored. so i took 2 minutes to do this haha..
0 = 30x + (1/3)(1-x)(-20) + (2/3)(1-x)(43/47)(-20) + (2/3)(1-x)(4/47)(3/4)(50) + (2/3)(1-x)(4/47)(1/4)(3/4)(110) + (2/3)(1-x)(4/47)(1/4)(1/4)(260)
So.. first we multiply out all of the parenthesis..
0 = 30x – 20/3 + 20x/3 – 1720/141 + 1720x/141 + 100/47 – 100x/47 + 55/47 – 55x/47 + 130/141 – 130x/141
Then we move all of the characters which don't contain x to the opposite side of the equation.
20/3 + 1720/141 – 100/47 – 55/47 – 130/141 = (30)x + (20/3)x + (1720/141)x – (100/47)x – (55/47)x – (130/141)x
Knowing that 141 is the multiple of prime numbers 3*47; we know the LCD (lowest common denominator) of these characters is 141. so each term is multiplied by 1 in the form of whichever it lacks ( ie. 20/3 is multiplied by 47/47 to get (20*47)/(3*47) = 940/141 )
940/141 + 1720/141 – 300/141 – 165/141 – 130/141 = x(4230/141 + 940/141 + 1720/141 – 300/141 – 165/141 – 130/141)
Then we can simply add together all of the numerators, as they have a common denominator:
2065/141 = x(6295/141)
Multiply each side by the reciprocal of the coefficient attached to x:
x = (2065/141)(141/6295)
And voila!
x = (2065/6295) = .3280381254964257…
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