# What does the fraction equal?

Here is a puzzle I just heard about.

Nebuchadnezzar x  Methuselah
---------------------------    =   ?
Melchior + Balthazar

• Looks like you have quite a few valid potential answers! – El-Guest Sep 8 '18 at 18:23
• I think dr jimbob's is clearly the intended one. – Gareth McCaughan Sep 8 '18 at 19:16

These are

large wine bottle sizes specific for sparkling wine.

Specifically,

Melchior = 24 standard bottles,
Balthazar = 16 standard bottles,
Methuselah = 8 standard bottles,
Jeroboam = 4 standard bottles.
Source

So the math works out to give

$\frac{20 \mathrm{bottles} \times 8 \mathrm{bottles}}{24\mathrm{bottles}+16 \mathrm{bottles}} = \frac{160\mathrm{bottles}^{2}}{40\mathrm{bottles}} = 4 \mathrm{bottles}$

Which going back to the word equivalency we find is equal to the word:

Jeroboam

• (Thanks. Was having trouble getting the spoiler formatting working.) – dr jimbob Sep 8 '18 at 18:17
• No problem! The spoilers are funny, they are indeed >! but you can't have consecutive lines of >! unless you have <pre> or some funny code before and after it. I like personally spacing things out with non-spoiler words. – El-Guest Sep 8 '18 at 18:19
• This is definitely the right answer in my view. Congratulations. – Anush Sep 8 '18 at 19:24

306.

This is because

of the ages of the men when they died: Nebuchadnezzar was 72; Methuselah was 969; Melchior was 116; and Balthazar was 112.

So the math works out to

$\frac{72 \times 969}{116 + 112} = 306$.

• Wow. Even though this wasn't the answer, it's pretty remarkable that you got an integer out of that. – greenturtle3141 Sep 9 '18 at 16:09
• @greenturtle3141 I was stunned when it worked out like that — to be honest, if it didn’t I might’ve not posted it haha! – El-Guest Sep 9 '18 at 16:14

I'm not sure if my answer is right, but this could be a variation

If we take the number word of each word (i.e. a=1, 26=z) and do the math we get: (148*112)/(83+89), to 96.3720930233