A few days ago
Algebra Problem?
On the planet ZOG, 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 coin. Also, suppose 1 green = n blue, 1 blue = n yellow, 1 yellow = n red, and 1 red = n white.
What is the whole number rate of exchange of these coins? Is only one exchange rate possible?
Top 1 Answers
A few days ago
Favorite Answer
The values of the colours indicated by their initial letters on the bais w = 1 are:
w = 1
r = n*1 = n
y = nr = n^2
b = ny = n^3
g = nb = n^4
Equating the exchangeable coins:
12w + 9r + 8y + 4b = 2w + r + b + g
Substituting for each letter in terms of n:
12 + 9n + 8n^2 + 4n^3 = 2 + n + n^3 + n^4
10 + 8n + 8n^2 + 3n^3 – n^4 = 0
n^4 – 3n^3 – 8n^2 – 8n – 10 = 0
I don’t see any whole number exchange rate possible for this equation.
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