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        riddles >> easy >> Shopping for Sunblock
        
(Message started by: SWF on Aug 14^th, 2006, 9:46pm)

Title: Shopping for Sunblock
Post by SWF on Aug 14^th, 2006, 9:46pm

On his way to visit one of his local California beaches SWF drops by the drug store to buy a bottle of sunblock. SWF is always looking for the best price possible, and the two cheapest bottles of sunblock per ounce are:

10 fluid ounce bottle (295.7353 milliliters) marked $7.05
and
300 milliliters marked $7.15

Other than price and quantity of sunblock inside, the two bottles are identical. Which bottle does he buy, and why?

Title: Re: Shopping for Sunblock
Post by Roy on Aug 14^th, 2006, 10:29pm

ooo_ooooohhh that's clever. I recall hearing something like that in my world tour #2.38495716

Unfortunately, it has been 20,000 years since i heard that........i hate that.

Title: Re: Shopping for Sunblock
Post by jollytall on Aug 15^th, 2006, 12:11am

Math would tell the second is cheaper. So it must be the first one you take.

Because the two bottles are identical (probably same brand, etc.) it is made on the same filling machine, but one is for the American market, one for the SI based market. The machine does not know which label it gets, so fills the same amount.
The labels do not lie, since there is always a +/- range and the small difference (less than +/- 1% from 298 ml, where the machine is probably set to) is acceptable.

The only point I don't get, how do they have a different price. I would assume in these cases the two labels get the same bar-code and thus the same price.

BTW posting #100 in the club. Good to be here.

Title: Re: Shopping for Sunblock
Post by towr on Aug 15^th, 2006, 12:24am

I'd take the first, I probably wouldn't use the whole bottle during a summer anyway.
And of course jollytail makes a good point.

Title: Re: Shopping for Sunblock
Post by Roy on Aug 15^th, 2006, 1:02am

1. rob the place

2. use your,'10% off of items over $7.00' coupon

3. Borrow a friends

Title: Re: Shopping for Sunblock
Post by Grimbal on Aug 15^th, 2006, 2:19am

It reminds me of the guy who successfully sued a toilet paper producer bacause the paper rolls didn't have the number of sheets the packet claimed.

But even If the 300ml bottle holds only 296 ml, The difference is probably not enough.

Yeah, I'd say take the cheapest. It will be taken away by the airport security anyway.

Title: Re: Shopping for Sunblock
Post by rmsgrey on Aug 15^th, 2006, 7:11am

Since the prices are the same per quantity to the accuracy of the currency (in other words, using either price to calculate what the other should be will give the listed price when rounded to the nearest cent) the (roughly) 1 part in 4300 difference in actual value is going to be swamped by any differences in usage.

The correct calculation is cost per application, and for most people, they'd get the same number of applications out of each bottle, making the cheaper bottle the better buy. Of course, if SWF is actually going to use the last little dribble from the bottle as a fraction of an application by combining it with some from a new bottle, then he's possibly better off with the larger bottle.

Of course, the next question is whether he'll use the ~300ml of sunblock, or whether he'd actually have been better getting a 150ml bottle for $5.00 and still throwing some of it away later...

Title: Re: Shopping for Sunblock
Post by SWF on Aug 15^th, 2006, 5:13pm

For purposes of brevity I have left out full clarification in the original statement of the question.

"Other than price and quantity of sunblock inside, the two bottles are identical." means that the two bottles really do have different amounts inside, and they contain exactly the quantities advertised. SWF is going to use every drop in whatever bottle buys. One way to do this is to cut apart the almost empty bottle and scrape off every bit of remaining residue.

SWF just wants to buy sunblock and go to the beach while making the logical choice, even though the difference in price may involve a fraction of a cent per ounce. The peace of mind in making the smart choice is worth more than the small amount of money involved. For purposes of this riddle consider the value of the sunblock only-- the value of an empty bottle and lid may be assumed to be zero. The income earned by investing the price difference in a low load mutual fund until a new bottle is needed should not be included in any calculations.

I still haven't seen the answer I am looking for. By the way, we seemed to hurting for new riddles around here so I was just trying to supply one.

Title: Re: Shopping for Sunblock
Post by Roy on Aug 15^th, 2006, 6:04pm

Yes, the riddle riverbed is drying up, or the dam has been closed off for the moment and we're all pounding at the wall. I like metaphors

Title: Re: Shopping for Sunblock
Post by Grimbal on Aug 16^th, 2006, 12:58am

[hide]Considering that he is going to a California beach where they charge exorbitant prices for everything, he should not only take the larger bottle, but even take two.
[/hide]

Title: Re: Shopping for Sunblock
Post by Weazel on Aug 16^th, 2006, 3:25pm

[hide]The first bottle gives a value of 41.948 mL per dollar, while the second bottle gives a value of 41.958 mL per dollar which gives us the assumption that the second bottle is the better deal.

However, California has a 7.25% minimum sales tax. Factoring that in, the costs become $7.56 and $7.67 respectively. This changes the values of the bottles to 39.118 mL and 39.113 mL, respectively, making the first bottle slightly a better deal.[/hide]

Title: Re: Shopping for Sunblock
Post by SWF on Aug 16^th, 2006, 5:32pm

Very good Weazel. You are correct.

Your statement that California has a "minimum" 7.25% sales tax does bring up a good point. If buying in Los Angeles County, for example, the tax is higher and the cheaper bottle changes.

Title: Re: Shopping for Sunblock
Post by towr on Aug 17^th, 2006, 1:13am

Aren't prices usually inclusive?

Title: Re: Shopping for Sunblock
Post by SMQ on Aug 17^th, 2006, 6:03am

With a few exceptions (gasoline and concession stands come to mind), prices in the U.S. are generally given before any sales tax is applied, or at least that's been my experience here.

--SMQ

Title: Re: Shopping for Sunblock
Post by towr on Aug 17^th, 2006, 6:12am

on 08/17/06 at 06:03:12, SMQ wrote:

With a few exceptions (gasoline and concession stands come to mind), prices in the U.S. are generally given before any sales tax is applied, or at least that's been my experience here.

Damn, that must be annoying. I already can't stand it when the additional 'removal tax' and delivery costs for largish electronic devices aren't included. I want to know what I'll actually pay to get an item, without having to use a calculator. I feel terribly cheated when I think I spot a good deal, and suddenly there's all those extra costs heaped up.

Title: Re: Shopping for Sunblock
Post by Icarus on Aug 17^th, 2006, 3:39pm

Yes. It is very annoying. Even for single purchases you can never be sure how much you will actually be paying until you pay for it (or bring that calculator along). But by displaying the pre-tax price, merchants can make it seem that their products are cheaper. In particular, if one merchant displays the post-tax price, and another the pre-tax price, the more gullible will buy from the pre-tax merchant, even if the price is really slightly higher. So no one wants to break the trend, even if it would be better for their customers.

Title: Re: Shopping for Sunblock
Post by SWF on Aug 17^th, 2006, 5:10pm

If you buy a computer monitor in California, on top of the advertised price, they will add sales tax and a monitor disposal fee of around $20. The store collecting the monitor disposal fee does not dispose of your monitor for you and can't even tell you who to get rid of it. When you find a place that takes monitors for disposal, they will charge you to accept it. And of course the money used to buy that monitor in the first place was subjected to federal income tax, state income tax, state disability insurance tax, social security tax, and medicare witholding.

Title: Re: Shopping for Sunblock
Post by BNC on Aug 17^th, 2006, 10:11pm

It could be solved by law requiring everyone to display full price (it is so in Israel).

A few years back, there was consumer up-rise against the airline companies. You could see an advertisement stating a flight for, say, $200. When paying, you'll hear: "but that's not including airfield cost, commission, traveling tax, VAT, whole-wing addition ;) ...." and end up applying $350.
The Keneset (Israel parliament) issued a law requiring full price for flight advertisments. Problem solved.

Title: Re: Shopping for Sunblock
Post by towr on Aug 18^th, 2006, 1:25am

on 08/17/06 at 15:39:47, Icarus wrote:

In particular, if one merchant displays the post-tax price, and another the pre-tax price, the more gullible will buy from the pre-tax merchant, even if the price is really slightly higher. So no one wants to break the trend, even if it would be better for their customers.

One part-solution would be to show both the inclusive and exclusive price. I mean, they do it when there's a discount (before <a lot> now <cheap>), because you have to show how much you save.
Although that may still confuse some customers.

We still have the problem with airprices here though, only sales taxes is included in prices, not all the extra additions. But our consumer union is lobbying to have a law passed to remedy that. I hope they meet with the same success as the people in Israel. Not that I fly much, but in general principle, and possibly it'll straighten out other areas too.

Title: Re: Shopping for Sunblock
Post by graphia on Aug 18^th, 2006, 1:47am

on 08/17/06 at 22:11:04, BNC wrote:

A short while back an airline got into a lot of trouble from the Commerce Commission here in New Zealand for advertising prices that were about half the real price, it's just a complete con if they get away with that.

Title: Re: Shopping for Sunblock
Post by jollytall on Aug 19^th, 2006, 1:48pm

on 08/16/06 at 15:25:09, Weazel wrote:

Thanks God, I am not familiar with the US tax rules. But in my country I would assume if they would call it a MINIMUM tax, it would mean that the actual tax applied CANNOT be less than that. No shopkeeper would want to charge more either, so more or less they would charge that rate. But then comes the rounding.
If the intention of the lawmaker is to add 7.25% and round it to cents using common rounding rules then he would say so. So with my common sense logic, the lawmaker uses "minimum tax rate" term meaning that you always have to round up the gross amount, which in this example would be 7.57 in the first case and that would reverse the logic. But I guess a similar riddle could be composed working even with these parameters.

Anyway, thanks to introduce us to the US tax system.

Title: Re: Shopping for Sunblock
Post by honkyboy on Aug 19^th, 2006, 3:27pm

I work as a bartender in the US. Some things we sell are advertised full price (alcohol) others are pre-tax (food). It can make for some confusince instances.
Because of rounding our computer system prices one beer at $2.50 (advertised price) and two at $5.01. I have never been able to explain to a tipsy person that I am not trying to rip them of for a penny.

This is also the country where gas stations sell you gas measured in thousandths of a gallon. If only fuel flow meters were that accurate . . .

Title: Re: Shopping for Sunblock
Post by SWF on Aug 19^th, 2006, 4:50pm

I think "minimum" of 7.25% means the rate will be at least 7.25% anywhere in California. That is the state sales tax rate. Some places also have a county ro city tax, so sales tax in those areas would be greater than 7.25%.

In the US, gasoline is usually priced to a non even number of cents per gallon, with the fractional cent per gallon always 0.9. Do other countries do that?

Title: Re: Shopping for Sunblock
Post by honkyboy on Aug 19^th, 2006, 5:10pm

on 08/19/06 at 16:50:23, SWF wrote:

In the US, gasoline is usually priced to a non even number of cents per gallon, with the fractional cent per gallon always 0.9. Do other countries do that?

Yes, with the final price rounded to the nearest cent.

*A few years ago I did work for a company in the US that made the fuel metering systems for gas pumps. They were trying to improve there metering systems to be in line with US regulations and match the new digital pump read outs displaying three decimals. Most at the time were of by around +/- 0.003 depending on the rate of fuel being pumped.

Title: Re: Shopping for Sunblock
Post by Icarus on Aug 20^th, 2006, 2:15pm

That is a little different than what SWF is talking about, I think.

Gas prices here in the US are always chosen with an addition $0.009 or 0.9 cent addition. So instead of have a gas price $2.99 per gallon, the price we have $2.999 per gallon (usually this is expressed with the last digit raised: $2.99⁹). We never have prices with anything other than that 0.9 cent extra: it is never $2.99⁷ or $2.99³, and never, ever just $2.99.

Gas stations got in the habit of adding the 0.9 long ago (at least as far back as the 1940s or 1950s) because it made their prices seem smaller than they really were. (Back then, 1 cent was about 10% of the price per gallon!)

Title: Re: Shopping for Sunblock
Post by truemuffinman on Aug 21^st, 2006, 9:00pm

[hide]At those prices, SWF decided to buy ingredients to make his own sunblock, which totalled $6.07, thus saving money.[/hide]

;)

Title: Re: Shopping for Sunblock
Post by Roy on Sep 1^st, 2006, 12:29am

I thought that aswell, but didn't know how much it would cost