Question

You are watching a game of poker on ESPN with your friends. You are trying to figure out the value of each colored chip that is being played. Supposed 12 white, 9 red, 8 yellow, 4 blue, and 0 green chips can be exchanged for 2 white, 1 red, 0 yellow, 1 blue and 1 green chip. Also. supposed 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 for these chips?

is only one exchange rate possible?​

Answer 1

9514 1404 393

Answer:

  N = 5; only one rate is possible

Step-by-step explanation:

The values of the sets of chips are ...

  12 +9N +8N^2 +4N^3

and

  2 +N +N^3 +N^4

We want to find N such that the difference in value is zero:

  N^4 -3N^3 -8N^2 -8N -10 = 0

A graphing calculator can show us the roots. There is only one positive real root to this equation: N = 5.

The exchange rate N is 5. Only one rate is possible.