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?

17

To find out how much Vanna charges for each vowel, we need to determine the individual price for each vowel.

Let's start by taking a look at the words given:
- Audacious sells for $260
- Equivocations sells for $340
- Inimitable sells for $225
- Onomatopoeia sells for $435
- Unambiguous sells for $225

We know that the cost of each vowel is less than $250 and that consonants are free.

To find the cost of each individual vowel, we'll need to compare the prices of words with different vowels.

Let's consider the word "Inimitable" and the word "Unambiguous." Both words have the same price of $225, which suggests that both words have the same number of vowels.

Since "Inimitable" and "Unambiguous" have different vowel compositions, we can conclude that there are two vowels in each, and each vowel in these words costs $112.50 ($225 / 2 = $112.50).

Next, let's consider the word "Onomatopoeia" and compare it to the word "Inimitable."

Since "Onomatopoeia" sells for $435 and "Inimitable" sells for $225, we can see that the cost difference between the two words is $210.

Since "Onomatopoeia" has three additional vowels compared to "Inimitable," we can conclude that the cost of each additional vowel in "Onomatopoeia" is $70 ($210 / 3 = $70).

Now, let's determine the price of each vowel by comparing the remaining two words, "Audacious" and "Equivocations."

Since the cost of "Onomatopoeia" with its nine vowels is $435, and the cost of "Equivocations" with its four vowels is $340, we can see that the additional five vowels in "Onomatopoeia" cost $95 ($435 - $340 = $95) in total, which means each additional vowel costs $19 ($95 / 5 = $19).

Finally, we can find the price of the first vowel in "Audacious" by subtracting the prices of vowels in "Equivocations" and "Onomatopoeia" from the total price of "Audacious."

Since "Equivocations" and "Onomatopoeia" contribute a total cost of $95 for their five additional vowels, we can subtract this from the total price of "Audacious" to find the cost of the first vowel: $260 - $95 = $165.

Based on all the calculations above, we have determined the prices for each vowel:

- The price for the first vowel (a) is $165
- The price for the second vowel (u) is $19
- The price for the third vowel (i) is $19
- The price for the fourth vowel (o) is $19
- The price for the fifth vowel (e) is $19

Therefore, Vanna Red charges $165 for the letter a, and $19 for each of the vowels u, i, o, and e.