Poll of the Day > Check my math please

(+) Yeah! (+)

Hello, friends. I'm into my second 24 hours of awakeness, spent the last far too long trying to figure this out, so please check my math for the following word problem.

I had $7. The store sold 12 packs of beer X for $6.09, with beer X being 5.5% alcohol and 12oz per can, but also sold 4 packs of beer X+! at $2.29. Beer X+! is 8% alcohol, but also 16 oz per beer.

I, being an alcoholic, want to maximize my ounces of alcohol per dollar spent. Sadly, my insomnia, combined with having purchased 3 of the X+! 4 packs and drinking some of them, has blown a gasket in my head. I want to know which option provides the more bang for the buck. My reasoning is as follows:

Conditions:
Y: 4 packs of beer, 16 oz/beer, at 8% alcohol (i.e. 0.08 oz alc/1 oz beer), $2.29/4 beers
Z: 12 packs of beer, 12 oz/beer, at 5.5% alcohol, $6.09/12 beers

Y = 12 beers * 16 oz beer/beer = 192oz beer
at 8% alcohol/beer, for Y :
Y = 192 oz beer * 0.08 oz alc/oz beer = .08 oz alc * 192 = 15.36 oz alc

Z = 12 beers 12 oz/beer = 144oz beer
at 5.5% alcohol/beer, for Z:
Z = 144 oz beer * 0.055 oz alc/oz beer = 144 * .055 oz alc = 7.92oz alc

Y also = $6.87 (3 for packs at $2.29 each)
Z also = $6.09 (1 12 pack at $6.09)

Y = $6.87 = 15.36 oz alc = $6.84/15.36 oz alc = $0.44/oz alc
Z = $6.09 = 7.92 oz /al = $0.77/oz alc

Accordingly, and as I said, I bought 3 of the X+!. Good? Yes or no, please show your work.
---

Wrong.
---

Show your work
---

I have to go stick needles in my cat by proxy. I will be back shortly.
---

Lobotomy_Jack posted...

I have to go stick needles in my cat by proxy.

lmao, what
---

Lobotomy_Jack posted...

Show your work

Im not doing your homework for you
---

She needed a rabies vaccination. I wasn't going to do it.
---

first determine the total amount of beer.

X=12*12 or 144 oz

X1=12*16=192

Then multiply those by the percentage of alcohol. You actually don't even need to do that though since X1 has both more ounces AND more alcohol per ounce, since both numbers are larger, the end result would also be significantly larger.

In the end, you are almost getting twice the amount of actual alcohol from X1, for a tiny bit more money.

Of course taste should factor in as well, but if your drunk enough, it probably won't matter much.
---

Right, but the price wasn't (exactly) the same.

I'm pretty sure I went the right way, but am more interested at knowing if I got the right comparative values because...well, pedantry.
---

Cost
X - 6.09 / 12 = 0.5075 cents a can

X! - 2.29 / 4 = 0.5725 cents a can

Cost per ounce
X - 0.5075 / 12 = 0.042 cents

X! - 0.5725 / 16 = 0.035 cents

Alcohol per dollar
X - 0.042 / 5.5% = 0.00231

X! - 0.035 / 8% = 0.0028

1 X vs 3 X!
X - 0.00231 x 12 = 0.02772 cents worth of alcohol

X! - 0.0028 x 12 = 0.0336 cents worth of alcohol

Price per 12 x cwoa
X - 6.09 x 0.02772 = 0.1688

X! - 6.87 x 0.0336 = 0.2308

Result - X! gives you more alcohol by single 4 packs oherwise you're better off with X
---

I like this topic.

Hmm, I agree with your conclusion, but your math feels wrong.
---

I should elaborate: $.77 vs $.44 seems to steep. I would like to know if it is in fact wrong, and if so where I went wrong.

I tried to keep units consistent...
---

Hmmmm

How do we compare $6.87 worth of X to X! ?
---

by ounce of alcohol per overall volume...per dollar
---

Im too hungover to do the math, but I feel like for a total difference of 78 cents theres no way the 12 pack of X was a better option than X! given a total of 48 extra ounces and a stronger ABV.

The problem is that X (or X!) isnt available in the same amount as the other.. even if you do the math, the cashier isnt going to open a 13th or 5th can respectively just for you

You either pay the standard/base amount for X for less or more $ for X!
---

Basically you pay about 10% more for 3*X1 then you do for X.

Meanwhile you get 33% more ounces of beer AND slightly over 40% more alcohol content per ounce (which means double the alcohol content since you get more ounces.

So basically for 10% more cost, you end up netting 50% more alcohol content, which seems to be what you are interested in.

It's very worth it.
---

Lmao