If consonants are free, determine the cost of the five vowels A, E, I, O, and U from the following clues:

Audacious costs $260 Equivocation costs $340 Inimitable costs $255 Onomatopoeia costs $435 Unambiguous costs $225




Solution:

The answer is:
a = $60
e = $75
i = $40
o = $50
u = $25

 

To solve it, I set up 5 simultaneous linear equations: (I used brackets to indicate each equation) 2a + i + o + 2u = 260 [1] a + e + 2i + 2o + u = 340 [2] a + e + 3i + = 255 [3] 2a + e + i + 4o = 435 [4] a + i + o + 3u = 225 [5] 3*[2] - [5]: 2a + 3e + 5i + 5o = 795 [6] -2*[2] + [1]: - 2e - 3i - 3o = -420 [7] [4] - 2*[3]: - e - 5i + 4o = -75 [8] [6] - 2*[3]: e - i + 5o = 285 [9] [8] + [9]: - 6i + 9o = 210 [10] [7] + 2*[9]: - 5i + 7o = 150 [11] 5*[10]: -30i + 45o = 1050 [12] -6*[11]: 30i - 42o = -900 [13] [12] + [13]: 3o = 150 o = 50 then substitute back to find i = 40, e = 75, a = 60, and u = 25.

You could also solve this with Cramer's Rule or with a computer program:
Click here to see Keith Mealy's computer program




Correctly solved by:

1. Rick Jones Kennett Square, Pennsylvania
2. Richard Johnson * La Jolla, California
3. Keith Mealy * Cincinnati, Ohio
4. Joe Heintz Manchester, Tennessee
5. John C. Funk Ventura, California
6. David Dixon Bennettsville, South Carolina
7. Bill Hall Wellington, Florida
8. George Gaither Winchester, Virginia
9. ---------- Feltham, Middx, United Kingdom
10. Chip Schweikarth Winchester, Virginia
11. Bob Hearn Winchester, Virginia
12. Erin McGinnis Winchester, Virginia
* Wrote computer programs to solve the problem