# Finding the value of each color?

1. Oct 13, 2014

### Avraker

1. The problem statement, all variables and given/known data
Ok, so a friend of mine gave me this, I already failed, even tho I think I came pretty close, but I did something wrong along the way.
I have not done math in like 8 years so,... yea xD I feel like a failiure.

Since I hate not knowing the answer, and my friend won't tell me, I thought I would come to you guys ^^

I need to find the value of each color. I'll assign each color a letter.

Red=R
Light Red=X
White=W
Light White=H
Yellow=Y
Purple=P
Light Purple=D
Blue=B
Green=G

I do have the value of one color.
White = 9

2. Relevant equations
R=B-P

2Y=B

H=2R + G

Y + D=2R + X

R + P=B

D=G + B

2B=D

2R>Y

3R=W

X + Y=2W

P<R + Y

X + B=R + H

R + Y + W=P

W= Y + P

P + W=X

R + B=G

X + R=H

R + 2Y=G

_________________

So I need the Value of each color :O

Would be so happy if someone could help me, so I could know the answer, since he won't tell me ><

Thank you for taking your time!

2. Oct 13, 2014

### GFauxPas

Start by replacing each W with 9.

3. Oct 14, 2014

### haruspex

Are theere no constraints on the ranges? E.g. Does each have to be a whole number?
The equations are not independent, i.e. some can be deduced from others, so are redundant.
A good way (after substituting for W, as GFauxPas suggests) is to write each equation with unknowns on the left and constants on the right. (Leave out the inequalities for now.) So 2B=D becomes 2B-D=0. You can then write the equations in matrix form. This will help you spot equations relating the same few variables. You can then add and subtract rows etc. to see if some rows can be reduced to all zeroes, allowing you to eliminate those rows. Further such manipulation may allow you to extract some specific values, but I suspect that after getting rid of the redundant equations you will have less than eight left.

4. Oct 14, 2014

### skiller

Some of those equations look inconsistent to me.