On the planet ZOG, coloured coins are used for money. see below?
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On the planet ZOG, coloured coins are used for money. Suppose 12 white, 9 red, 8 yellow and 4 blue coins can be exchanged for 2 white, 1 red, 1 blue and 1 green coin. Also, suppose 1 green= x blues, 1 blue= x yellow, 1 yellow = x red and 1 red = x white. What is the whole number rate of echange for these coins?"
On the planet ZOG, coloured coins are used for money. see below?12w+9r+8y+4b=2w+1r+1b+1g
10w+8r+8y+3b=1g
g=xb
b=xy
y=xr
r=xw
10w+8wx+8wx^2+3wx^3=wx^4
10+8x+8x^2+3x^3=x^4
(-1)x^4+(3)x^3+(8)x^2+(8)x+(10)=0
x=5
w=1
r=5
y=25
b=125
g=625
On the planet ZOG, coloured coins are used for money. see below?Since there is no particular color of coin that's designated as representing ONE dollar (or Zollar or whatever...) I think it's easiest to just pick one. So let's take the value of a white coin and call that "1". This is arbitrary, but I think it simplifies things. Now, the hardest part of this type of problem is often writing it out in equations. So:
12+9R+8Y+4B = 2+R+B+G
G=xB
B=xY
Y=xR
R=x
Where R is the value of a red coin, measured in white coins, etc.
By simple substitution:
R=x
Y=x^2
B=x^3
G=x^4
Now we can write the long equation as:
12+9x+8x^2+4x^3 = 2+x+x^3+x^4
Moving everything to one side:
x^4 - 3x^3 - 8x^2 - 8x - 10 = 0
So now you just have a 4th degree polynomial. The simplest method is to graph it and look for whole-number roots.
On the planet ZOG, coloured coins are used for money. see below?x=5 (to finish Matrix's solution).
Steve
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