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Help with Pre-Calculus Math homework (+10 points)?
On the Planet PAL, colored coins are used for money. Suppose 12 white, 9 red, 8 yellow, 4 blue, and 0 green coins can be exchanged for 2 white, 1 red, 0 yellow, 1 blue, and 1 green coins.
Also suppose:
1 green= n blue
1 blue= n yellow
1 yellow= n red
1 red = n white
what is the whole number rate of exchange of these coins? is only one exchange rate possible?
+10 points to who ever can help me SET IT UP and also SOLVE IT.
Denote the coloured coins by their first letter, then
12w + 9r + 8y + 4b + 0g = 2w + 1r + 0y + 1b + 1g
or g = 10w +8r +8y +3w
Now g = n^4w, b = n^3w, y = n^2w & r = nw
So n^4w = 10w + 8nw + 8n^2w + 3n^3w
Dividing throughout by w, we get
n^4 = 10 + 8n + 8n^2 + 3n^3
A little exploration yields n = 5 and since n has to be positive, only one exchange rate is possible
Ans: One exchange rate, n = 5