SOLUTION: On planet ZOG, colored coins are used as money. 12 white, 9 red, 8 yellow, 4 blue, and no greens can be exchanged for 2 white, 1 red, no yellows, 1 blue, and 1 green. Suppose tha
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Question 428371: On planet ZOG, colored coins are used as money. 12 white, 9 red, 8 yellow, 4 blue, and no greens can be exchanged for 2 white, 1 red, no yellows, 1 blue, and 1 green. Suppose that 1 green=n blues, 1 blue=n yellows, 1 yellow=n reds, and 1 red=n whites.
What is the whole number exchange rate for these coins? Is one exchange rate possible?
Okay, so I started work and hit a dead end. My work is as follows.
therefore
We also know that g=bn, b=ny, y=nr, and r=nw.
Therefore
or by subtracting everything to one side and dividing everything by w.
The problem is this: I am in Algebra I. We haven't learned how to solve 4th degree polynomials, which makes me think that there is an easier way to solve this problem that I didn't pick up on.
Please help. I don't necessarily want the answer, just an Algebra I way to solve this problem.
Thanks in advance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
On planet ZOG, colored coins are used as money. 12 white, 9 red, 8 yellow, 4 blue, and no greens can be exchanged for 2 white, 1 red, no yellows, 1 blue, and 1 green. Suppose that 1 green=n blues, 1 blue=n yellows, 1 yellow=n reds, and 1 red=n whites.
What is the whole number exchange rate for these coins? Is one exchange rate possible?
Okay, so I started work and hit a dead end. My work is as follows.
therefore
We also know that g=bn, b=ny, y=nr, and r=nw.
Therefore
or by subtracting everything to one side and dividing everything by w.
The problem is this: I am in Algebra I. We haven't learned how to solve 4th degree polynomials, which makes me think that there is an easier way to solve this problem that I didn't pick up on.
Please help. I don't necessarily want the answer, just an Algebra I way to solve this problem.
Thanks in advance.
==============================
1st of all: There is a solution less than 10.
2nd: Let n = some value like n = 10. You might
get a positive value.
Let n = some value like n = -10. You might
get a negative value.
----
That mean there is a solution between n = -10
and n = 10.
---
Use that idea to pin the solution between 2
values. Keep pinning it till you find the
solution.
======================
By the way, you have done a find job with
the problem. Congratulations.
Cheers,
Stan H.
================
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