“A times C equals 270. D times E equals 440. What does F equal and why?”
I would suggest that we are dealing with notes hear, because A = 440 Hz, except that the closest notes to 270 Hz are C ~= 261 Hz, and Db ~= 277 Hz.
from: http://ccrma-www.stanford.edu/CCRMA/Courses/220a/unjung/wellScale.html
Ah well.
askol, you’re mixing up the OP’s question, and a similar one I have an answer for. I was hoping Mahaloth misremembered some of the details of the question.
By the way, here’s the answer to “A times C equals 270. D times E equals 450. What does F equal and why?”
F = 24. A, C, D, and E are musical notes with frequencies 15, 18, 20 and 22.5 (yeah, that doesn’t match up with A440, but the ratios are all correct.)
Instead of “What does F equal and why?”
try
“What does F equal?And Y?”
This can be applied to the numbers as well. Two hundred and seventy generally means 270 units of one type. But it could mean two hundred units of one type and seventy units of another type.[sub]fer example[/sub] Two hundred slices of pizza and seventy cans of Dew.
I second Saltire’s request for a clarification of exactly how the numbers were said.
I, on the other hand am unimaginative enough to attempt to solve this as a series with a missing member.
So the first assumption I made is that a third multiplication statement is implied by the first two.
I began by factoring both 270 and 440. I noticed that each can be reached by multiplying a number with a perfect cube (3[sup]3[/sup] X 10 = 270, and 2[sup]3[/sup] X 55 = 440). Furthermore, the order in which the perfect cubes is presented suggests a sequence that offers the third perfect cube in the series (1[sup]3[/sup], or 1).
Having teased out one series of multipliers, I set about looking for the other one. Trying to justify considering 10 and 55 as two numbers in a series, I note that 10 factors as 5 X 2, and 55 factors as 5 X 11. If I make 5 the factor that remains constant, I can look for something that logically follows from 2, 11 as number three in the series. Well, 11 = (5 X 2) + 1, and there’s a 5 again!
So, if the reason for the second number is multiplying 5 by the sum of the first number and 1, [55 = 5 X ((5 X 2) -1)], then the third number should be 230 [230 = 5 X (55 + 1)].
So, if my logic holds, *f/i] = either 1 or 230.
Of course, it probably doesn’t apply. But it strikes me that we’re being asked to solve for f with very little guidance as to the actual assumptions we need to make.
F equals…
PHI
F equals…
PHI
I had thought about it being “Y” instead of “Why”.
I can only say that it was said, “And Why(Y)?”.
It could very well be a trick.
Ok,
Here’s my dumb answer. I assumed that in addition to
AB=270 and CD=440
that there was a linear relationship between A B C D E and F. To wit C(n)=an+b, C(n) represents the variables A through F. So,
C(0)=A=b
C(1)=B=a+b
C(2)=C=2a+b
C(3)=D=3a+b
C(4)=E=4a+b
C(5)=F=5a+b
If anyone is keen on solving the cubic equation for b that results, you’re better than I. I used the goal seek tool in Excel and found the following values
A=15.33675
B=17.60477
C=19.8728
D=22.14082
E=24.40884
F=26.67687
From which, AB=270, CD=440, and EF=651.1515, which is fairly unsatisfying.
There are probably a couple more solutions to this cubic equation as well.
If you use askol’s version of the question (“A times C equals 270. D times E equals 440. What does F equal and why?”) and NotMrKnowItAll’s method, except assume the letters are keys on the piano and include the black keys, you get
A = 15
C = 18
D = 20
E = 22
F = 23
Getting closer…
Mahaloth, is this question being asked over and over as part of a contest? Otherwise, you know you’re going to have to call the station and find out the answer for us, don’t you?
Answer: F=29. It is the value of the letter-series U.S. postage stamp issued to deal quickly with the first-class rate increase to 29¢. Over the years, A=15¢ B=18¢, etc.
It was finally given on the radio.
Good one!