Vanna Red sells the vowels a, e, i, o, and u each for a different

price but less than $250. Consonants are free. You must pay
separately for each occurrence of a vowel in a word. Audacious
sells for $260, equivocations for $340, inimitable for $225,
onomatopoeia for $435, and unamibiguous for $225. How much does
Vanna charge for each vowel?

Here's what I came up with...strictly by trial and error. You might want to check to be sure it works out.

a = 30
e = 75
i = 40
o = 30
u = 55
Like I said, be sure it works out.

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To find out how much Vanna charges for each vowel, we can compare the prices of different words that contain the same vowels.

From the given information, we have the following prices:
- Audacious: $260
- Equivocations: $340
- Inimitable: $225
- Onomatopoeia: $435
- Unambiguous: $225

Let's compare the prices of words that have similar vowels:

1. In the words Audacious and Inimitable, the vowels a, i, and u appear.
- The price difference between Audacious and Inimitable is $260 - $225 = $35.
- These two words have the same vowels, except for the vowel o in Audacious.
- Therefore, Vanna charges $35 for the vowel o.

2. In the words Audacious and Unambiguous, the vowels a and u appear.
- The price difference between Audacious and Unambiguous is $260 - $225 = $35.
- These two words have the same vowels, except for the vowel i in Audacious.
- Therefore, Vanna charges $35 for the vowel i.

3. In the words Inimitable and Unambiguous, the vowels i and u appear.
- The price difference between Inimitable and Unambiguous is $225 - $225 = $0.
- These two words have the same vowels.
- Therefore, Vanna charges $0 for the vowel o.

Now, let's determine the prices for the remaining vowels:

4. In the word Equivocations, the vowels e, i, and o appear.
- We know that Vanna charges $35 for each occurrence of the vowels i and o.
- The price difference between Equivocations and Inimitable is $340 - $225 = $115.
- The price difference of $115 includes two vowels, i and o, since they appear in both words.
- Therefore, Vanna charges $115 - ($35 + $35) = $45 for the vowel e.

To summarize, Vanna charges the following amounts for each vowel:
- a: $35
- e: $45
- i: $35
- o: $35
- u: $0

To determine how much Vanna charges for each vowel, we can compare the prices of different words and calculate the differences in price based on the number of vowels in those words.

Let's start by looking at the words "inimitable" and "unambiguous". Both words have the same price, $225, which means that they have the same total cost for vowels.

The word "inimitable" has 4 vowels, while "unambiguous" has 5 vowels. So, the extra vowel in "unambiguous" must have cost $0 since the total cost for both words is the same. Therefore, the price for each vowel is $45 ($225 / 5).

Now, let's compare the words "inimitable" and "onomatopoeia". The word "inimitable" costs $225, while "onomatopoeia" costs $435. The difference in price is $210, and there are 6 extra vowels in "onomatopoeia" compared to "inimitable". Dividing $210 by 6 gives us $35, which is the cost of each vowel.

Similarly, we can compare the words "inimitable" and "equivocations". The difference in price is $115, and there are 5 extra vowels in "equivocations" compared to "inimitable". Dividing $115 by 5 gives us $23, which is the cost of each vowel.

Finally, we can compare the words "inimitable" and "audacious". The difference in price is $35, and there is 1 extra vowel in "audacious" compared to "inimitable". Therefore, the cost of each vowel in "audacious" is $35.

To summarize:
- The cost of each vowel in "inimitable" is $45.
- The cost of each vowel in "onomatopoeia" is $35.
- The cost of each vowel in "equivocations" is $23.
- The cost of each vowel in "audacious" is $35.

Please note that we have made an assumption here that the cost of each vowel is the same throughout a word and that the cost of consonants is always free.