A few days ago
Anonymous

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
Anonymous

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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