CPhill

2/3 x 200/1 =

400/3  =    133 + 1/3   (if you prefer a mixed result...)

25%  = .25

So.....just put this into the onsite calculator

.25 x 670

√72  =

√(36 * 2) =

6√2

(x+[1+√2]) (x-[1-√2])  =

x^2 + x(1+√2) - x(1-√2) - (1+√2)(1-√2) =

x^2 + x + √(2)x - x + √(2)x - ( 1 - 2) =

x^2 + 2√(2)x + 1

I wonder if this isn't supposed to be

x - 40%(x)  =  317.27    ???   that's the the way I'm going to interpret it......!!!

So we have

x - .40x = 317.27      ( remember 40% = .40  )

.60x  = 317.27      divide by .60

x = 317.27 / .60

x = about 528.78

Thanks, Melody....at least there weren't any "inverse functions" involved......LOL!!!!

Call the full ship, 27 + x, where x is the number of prisoners....and if (1/2)x escape, then the number of people on the ship now equals 27 + (1/2)x ...therefore

27 + (1/2)x  = .85(27 + x)

27  + (1/2)x = 22.95 + .85x

4.05  = .35x

x = about 11.57

Sorry...I can't get the numbers to work, here....!!!!   (???)

Abs (a - b) will be largest when at least one of the other terms is minimized....so, since absolute value is always ≥ 0, let's minimize the middle term by letting b = c

This gives us

abs ( a - b)   + abs(c - a)  = 20   but, since  b= c, we can write

abs ( a - b)   + abs(b - a)  = 20  and let's assume  that a > b  [we could also assume the opposite....it won't matter]

So we have, using the definition of absolute value:

a - b  + -(b - a)  = 20

a - b  + a - b = 20

2(a - b)  = 20

(a - b)  = 10

Which implies that

abs (a - b) = 10

And that's as large as  abs(a - b) can be

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As Melody would say.......that's what I think..!!!.....of course....any constructive criticism is welcome....!!!