Vanna Black pays money for vowels. If consonants are worth nothing and the following words are worth the following amounts, then find the value of each vowel. All vowels are worth the same amount in each but each vowel has a different value.
Audacious=$260
Equivocation=$340
Inimitable=$255
Onomatopoeia=$435
Unambiguous=$225
Let a be the value of "a", e be the value of "e", etc. for i, o, and u.
Audacious has a u a i o u = 260. So 2a+i+o+2u = 260.
Do the same for the other 4 words; you have 5 equations for 5 variables.
To find the value of each vowel, we need to compare the words and determine the value difference between the vowels in each word.
Let's calculate the value of each vowel using the given words:
From the word "Audacious," we can see that the vowel 'A' has a value difference of $260-$55=$205.
From the word "Equivocation," we find that the vowel 'A' has a value difference of $340-$15=$325.
From the word "Inimitable," we see that the vowel 'A' has a value difference of $255-$25=$230.
From the word "Onomatopoeia," the vowel 'A' has a value difference of $435-$40=$395.
From the word "Unambiguous," the vowel 'A' has a value difference of $225-$55=$170.
Since each vowel has a different value, let's use the variable 'x' to represent the value of the vowel 'A.'
Based on the equations above, we can set up the following equation:
205x + 325x + 230x + 395x + 170x = 0
Simplifying the equation:
1325x = 0
Dividing both sides of the equation by 1325:
x = 0
This indicates that the value of each vowel is $0.
To find the value of each vowel, we can subtract the value of the consonants from the total value of each word and divide by the number of vowels. Let's calculate the number of consonants for each word:
1. Audacious: There are four vowels (A, u, i, o) and five consonants (d, c, s). Total consonant value is 0. So, the equation becomes (260 - 0) / 4 = 65.
2. Equivocation: There are six vowels (E, u, i, o, a, o) and six consonants (q, v, c, t, n). Total consonant value is 0. So, the equation becomes (340 - 0) / 6 = 56.66.
3. Inimitable: There are five vowels (I, i, a, e, e) and six consonants (n, m, t, b, l). Total consonant value is 0. So, the equation becomes (255 - 0) / 5 = 51.
4. Onomatopoeia: There are seven vowels (O, o, a, o, e, i, a) and seven consonants (n, m, t, p). Total consonant value is 0. So, the equation becomes (435 - 0) / 7 = 62.14.
5. Unambiguous: There are five vowels (U, a, i, o, u) and six consonants (n, m, b, g, s). Total consonant value is 0. So, the equation becomes (225 - 0) / 5 = 45.
Based on these calculations, we find that each vowel in each word is worth the following:
Audacious: Each vowel is worth $65.
Equivocation: Each vowel is worth approximately $56.66.
Inimitable: Each vowel is worth $51.
Onomatopoeia: Each vowel is worth approximately $62.14.
Unambiguous: Each vowel is worth $45.
Please note that the values above have been rounded to two decimal places.