Scrabble Math problem VERY DIFFICULT PLEASE HELP

[klabelle12]

I need help with this problem. Thank you in advance. Here it is:

My friends have changed the rules for Scrabble. In their rules, each letter has a positive whole-number value. No two vowels have the same value. No two consonants have the same value. It is possible for a vowel and a consonant to have the same value. Scoring is done differently than in regular scrabble. The points for the vowels are added up, then seperately the points for the consonants are added up. These two numbers are multiplied together to give the word score. A list of words and their word scores is shown below. Determine the letter value of each letter, then determine the value of the word problemsolving.

PLUM = 36
PLUME = 48
MELT = 15
ROME = 98
SAVE = 51
WEST = 20
LAME = 18
PLANE = 39
MELBA = 51
PIPER = 110
VIPER = 150
WESTERN = 70
OUT = 81
GREET = 40
PAPER = 66


So far I have narrowed it down that P, L, and M are either 1, 2, or 3 OR they are 3 numbers that add up to 12.

 

[SlipEternal]

For each line, rewrite it as follows:

(P+L+M)*(U) = 36
(P+L+M)*(U+E) = 48
.
.
.
(2P+R)*(A+E) = 66

Now, when you see factors that are the same (like in the first two lines, (P+L+M) is a factor), you can divide them out. So,:
\(\displaystyle \frac{\text{U+E}}{\text{U}} = \frac{48}{36}\) and thus \(\displaystyle U=3E\).

Keep simplifying expressions until you get your answer. It took me about ten minutes.