# What's The Problem - #3



## Michael in FtW (Jun 7, 2005)

*OVERVIEW of PROBLEM:* Converting flour weight to volume in a bread recipe

Consul had a good observation in Problem #2 about flour weight VS. volume. So - let's play with it!

The generally accepted *correct* way to measure flour is to use a dry ingredient measuring cup ... use a spoon to lightly sprinkle the flour into the measuing cup until it overflows, then level it off by running a straight-edge across it. _*No*_ dipping the measuring cup into the flour, and no tapping, shaking or thumping the cup to level it off! This is normally the way flour is measured in a recipe unless otherwise stated - such as in *Cookwise* by Shirley Corriher (see _Measuring_ on page 11).

*ASSUMPTIONS:* We need to make a few assumptions here to try to avoid me leading someone off in the wrong direction this time.

1. We are using US standard weights and measures ... 1 Cup = 16 Tablespoons, 1 pound = 16 ounces, and standard 5 lb bags of flour which are labeled 5-lbs - 80 ounces - 2.26 kg (2.26 kg is actually 2268 grams). 

2. The moisture content of the flour is NOT a factor. Neither is if the bag says "Pre Sifted". 

3. Using the standard method of measuring flour (above) - you will be within +/- 0.02 ounce by weight per 1 Cup of flour.

4. The "serving size" information on the side of the bag is correct for US measurements (cups, spoons) and only an approximate for the metric weight conversion due to rounding errors. 


*HELP:* You shouldn't need anything more than a simple calculator (paper and pencil also works) but here is a site that will help you with conversions if you need them: http://www.onlineconversion.com



*THE PROBLEM:*

You have a bread recipe that lists volumes for everything but the bread and wheat flour - and those are given in pounds and ounces .. and you don't have any scales. What to do?

The recipe calls for 
1-lb 1-oz Bread flour
1-lb 2-oz Wheat flour

You've got a 5-lb bag of each ... and while you scratch your head you read the information on the side of each bag.

BREAD FLOUR: A serving size is 1/4 cup (30g) - and there are 75 servings per 5-lb bag.

WHEAT FLOUR: A serving size is 3-Tablespoons (31g)- and there are 72 servings per 5-lb bag.

*Rounded to the nearest quarter-cup - how many cups of bread flour and wheat flour do you need?*

BONUS POINTS: How did you calculate your answer?


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## kitchenelf (Jun 8, 2005)

I'm gonna cheat and call my friend Michael in FW - be right back


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## Michael in FtW (Jun 8, 2005)

kitchenelf said:
			
		

> I'm gonna cheat and call my friend Michael in FW - be right back


 
Oh - come on Elf - it's not that hard if you think about it. Really no harder than: If Andy has 5 pennies and the elfen one has twice as many ... how many times can Elf throw in her 2-Cents worth?


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## lyndalou (Jun 8, 2005)

Michael,
This may be too simple an answer, but I tried not to read too much into all of the information you gave us.
I am really guessing, but since 1lb. 1 oz = 17 ounces. I am saying 2 cups 1 tbsp. of bread flour

1lb 2 oz = 18 oz.  so it would be 2 cups plus 2 tbsp. of wheat flour.

Is it more complicated than that?

Used a pencil and paper. Could have figured it out in my head though.


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## kitchenelf (Jun 8, 2005)

(I hate just a smiley is too short a reply)


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## Michael in FtW (Jun 8, 2005)

lyndalou - yep, it's a little more complicated than that!  

The problem is to figure out the difference between volume and weight - *what volume will equal what weight*. It appears that you assumed weight and volume were the same ... 1 Cup (8-oz volume) of flour is equal to 8-oz by weight. 

Andy got it wrong last night .... but after I pointed him in the right direction he got it right this morning. So, trying to not give the answer away, I'll just say that the information you need to solve the problem is on the side of the bags.


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## jkath (Jun 9, 2005)

hmmm. Still trying to figure it out.
I never did well in word/geometry problems.


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## Michael in FtW (Jun 9, 2005)

Don't feel bad - I never did figure out how the answer to 2X = 3Y wound up being 4!


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## jkath (Jun 9, 2005)

Funny how we don't think we need science or math, then we grow up and cook, and we need to utilize both!


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## lyndalou (Jun 9, 2005)

Oh, gosh. you're right Michael, that is what I did. I'll try one more time, probably take me hours, math is not my strong suite. Do I actually have to have a bag of wheat flour? I'll check the bag in the market when I go later.


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## thumpershere2 (Jun 9, 2005)

It's all greek to me. good luck all.


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## Alix (Jun 9, 2005)

OW! My brain hurts. I will be back shortly. I am finding my calculator.


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## Alix (Jun 9, 2005)

One cup of wheat flour and one and a 1/4 of bread? Did I go the wrong direction in my conversion? That sounds too small.


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## Michael in FtW (Jun 9, 2005)

lyndalou said:
			
		

> Do I actually have to have a bag of wheat flour? I'll check the bag in the market when I go later.


 
No .... doooh ....(me impersonating Homer Simpson slapping his forhead)  Go back and look at the problem again - I gave you the only important information on the side of the bag for the two bags of flour we are using in this problem. No need to buy any!

Alix: Yep, it is too small. Not sure what you did. Remember, this a baking question not a banking question ... you can't convert grams into Euros to get ounces.  If you want to work it out in metric and convert to lbs/oz - 5-lbs is actually 2268 grams. The actual weight of a serving size of Bread flour is 30.24g (they round it to 30) and the actual weight of a serving size of Wheat flour is 31.5g (they round it to 31). I'll explain more when I post the answer tomorrow night.


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## lyndalou (Jun 10, 2005)

Michael, I was kidding about having to buy flour. I have to tell you that I am stumped on this one. Too much math for me, I guess.  I am anxiously watching for someone to come up with the right answer, though. Good luck all.


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## masteraznchefjr (Jun 10, 2005)

lol ill figure it out. itll be a warm up for my precalc test i have today.  

so i got bread flour 3.98 cups 
and wheat flour 3.03 cups 

all i did was use ratios 

1 serving / .25 cups = 75 servings /X 
x = 18.75 cups 

18.75 cups /80oz = x/17oz 

x = 3.98 cups bread flour

1 serving / 3 tb = 72 servings / x 
x = 216 tb 

216 tb / 80 oz = x / 18 oz 
x = 48.6 tb 

48.6 / 16 = 3.03 cups


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## Charlotte (Jun 10, 2005)

I am no good at math - I will check with my 14 year old daughter and get back to you - she just got a 98 in her last test - grade nine math... ( now she will hate me if she gets this wrong! but it will show her that YES we use math in everyday life!)


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## luvs (Jun 10, 2005)

i'm too tired to think, so i'll have to re-read this later. i need a looooog nap first.


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## Alix (Jun 10, 2005)

ARGH! Michael, I think I did the conversions backward. I SUCK at this. LOLOLOLOL! 

To be honest you know what I would do? I would look at my bowl and start dumping stuff in it (keeping track as I go) and when it looked right I would go to town. PHOOEY! I hate it when I mess stuff up like this. I am going to take another crack at it and then wait for your solution. This is fun Michael, thanks.


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## subfuscpersona (Jun 10, 2005)

Michael in FtW said:
			
		

> *OVERVIEW of PROBLEM:* Converting flour weight to volume in a bread recipe
> 
> *ASSUMPTIONS:* We need to make a few assumptions here to try to avoid me leading someone off in the wrong direction this time.
> 
> ...


As a mathematically challenged little old lady, here's what I came up with. I think you will need
BREAD FLOUR: ~16 1/4-cup units OR ~4 cups
WHEAT FLOUR: ~12 1/4-cup units OR ~3 cups

Here's how I arrived at my answer...

The key points from Michael's post are 
> The "serving size" information on the side of the bag is correct for US measurements (cups, spoons) and only an approximate for the metric weight conversion
and
> the premise that 1 Cup = 16 TBS and therefore that 1/4 cup = 4 TBS (this is correct for liquids but not necessarily for solids like flour)

step 1: convert flour measurements to oz
REQUIRED AMOUNT IN OZ
Bread flour	17.00 oz (1 lb + 1 oz)
Wheat flour	18.00 oz (1 lb + 2 oz)

step 2: calculate what % of the total 5-lb flour sack is required, given the sack weight (80oz) and the required recipe amounts in oz
REQUIRED AMOUNT AS % OF 5LB FLOUR SACK
Bread flour	21.25% (17 / 80)
Wheat flour	22.50% (18 / 80)

Michael wants the answer in 1/4-cup units (rounded) so I can calculate the answer easily for *bread flour* since the serving size is in 1/4 cup units, there are a total of 75 servings in the sack and I need 21.25% (by weight) of the sack for the 17oz of bread flour called for in the recipe.
REQUIRED AMOUNT IN 1/4-CUP SERVING SIZE UNITS
Bread flour	15.94 1/4-cup units (75 * .2125)

*Wheat flour* is more complicated, since *the serving size is 3TBS* and Michael says to assume that there are *4TBS per 1/4 cup of flour*
There are a total of 72 servings in the sack and I need 22.50% (by weight) of the sack for the 18oz of wheat flour called for in the recipe.
so...
REQUIRED AMOUNT IN 3 TBS SERVING SIZE UNITS
Wheat flour 16.2 3-TBS units (72 * .225)

But now I have to get my units from the 3-TBS serving size on the sack to the 1/4 cup (4 TBS) measuring unit that Michael wants.
First, I'll calculate how much wheat flour I need using TBS as the unit of the measure. I get total of 48.6 TBS (16.2 * 3) TBS.

Next, I'll divide 48.6 TBS by 4 since we assume that it takes 4 TBS flour to get 1/4 cup flour. This gives me 
REQUIRED AMOUNT IN 1/4 CUP SERVING SIZE UNITS
Wheat flour 12.15 1/4-cup units (48.6 / 4)

======= COMMENTS =======

In baking, flour (and other solids) really should be weighed, not measured. For example, when I measure flour using level TBS into a 1/4 measure, it only takes me 3 TBS to make 1/4 cup, not 4 TBS. 

The purchase of a "plain vanilla" digital scale (about $30) would eliminate a lot of the head scratching that went on here (including mine!).

=  =  cheers to all =  =


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## Michael in FtW (Jun 11, 2005)

*The answer is:* 
  Bread Flour = 4 Cups
  Whole Wheat Flour = 3 Cups

Congrats go to masteraznchefjr, subfuscpersona, and Andy M! It was really interesting to see the different approaches used.  
And a bottle of hair restorer tonic to everyone who pulled their hair out trying to figure this one out!  

And I forgive everyone who called me a  ...  


Once again Shirley Corriher and *Cookwise* get most of the credit - after Consul's comments on the last problem. If you can estimate the weight of a cup of a certain type flour by how you measure it - why not be able to estimate the weight if you use a standardized method of measuring that you knew would put your volume measurment close to scale weight if you know the info on the side of the bag?

I know, I should be ashamed - the "trick" was to read the serving size information and the number of servings on the bag. Using 1/4 cup for one and 3 Tbsp for the other was a little mean of me. But, they are directly off 2 bags of flour I have. For the Bread flour I used the info off a bag of Gold Medal unbleached all-purpose, and for the Whole Wheat I used the info off a bag of Bob's Red Mill #1 Semolina for Pasta.

The methods I used when I thought this one up: 

*Tablespoons (Tbsp) *

This is probably the easiest one to figure out ....

1) Tablespoons per serving X servings per bag = total Tbsp per bag
2) Oz per bag / total Tbsp = weight per Tbsp (in oz)
3) Oz per Tbsp X 16 = Oz weight per Cup
4) Weight of flour needed (in oz) divided by the weight of a cup of flour (in oz) = number of cups needed

_This is where the 1 Cup = 16 Tbsp was most important_

Bread Flour:
4 Tbsp (1/4 Cup) X 75 Servings = 300 Tbsp
80 Oz / 300 = 0.2666 per Tbsp
0.266 X 16 = 4.267 oz  ... rounds to 4.25 oz per cup
1-lb 1-oz = 17-oz
17 / 4.25 = 4

Wheat Flour:
3 Tbsp X 72 = 216 Tbsp
80 oz / 216 = 0.37 oz per Tbsp
0.37 X 16 = 5.93 oz ... rounds to 6 oz per cup
1-lb 2-oz = 18-oz
18 / 6 = 3

*Cups*

This one is converting everything to cups is a different way ...

Bread Flour:
1) Since a 1/4 is 0.25 of a Cup and there are 75 1/4 cups
the number of cups per bag is 0.25 X 75 = 18.75 Cups
2) The weight of a Cup of flour is therefore the total weight divided by the number of cups ... 80 oz / 18.75 cups = 4.266 oz per cup .... rounds to 4.25 oz per cup
3) 1-lb 1-oz = 17-oz
4) 17 / 4.25 = 4 cups

Wheat Flour: _this one is a little trickier and takes an extra step ..._

1) 3-Tbsp is 0.75 of a 1/4 cup - so to convert 72 3-Tbsp servings into 1/4 cups servings ... multiply the number of servings X 0.75 .... 72 X 0.75 = 54 1/4 cup servings.
2) Convert 1/4 Cups to Cups ... 54 X 0.25 = 13.5 Cups
3) The weight of a Cup of flour is therefore the total weight divided by the number of cups ... 80 oz / 13.5 cups = 5.925 oz per cup .... rounds to 6.0 oz per cup
4) 1-lb 2-oz = 18-oz
5) 18 / 6 = 3 cups

Charlotte - I would be very interest in seeing how your daughter would solve this problem! Wonder how her math teacher would approach it ...??? 

*Conclusion:* I like scales for baking - and I really need to break down and get a digital model, my old analog cheap thing is really only good for jelly and jam sessions. But, if you don't have a set of scales and you want to try a recipe - it's nice to know you can get within the ballpark.


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## Charlotte (Jun 11, 2005)

Ahhhh Michael... it was fun to try!

Congrats to those who managed it! We gave up over here...


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## subfuscpersona (Jun 11, 2005)

*free office suite  I used to solve the problem*

Thank heaven for spreadsheets. If you don't have one, a most excellent *free* office suite called OpenOffice may be downloaded from http://www.openoffice.org/ It is just as good as Microsoft's office suite and has a word processor, spread sheet, presentation manager and lots of other goodies.

OpenOffice is available for Windows [Windows 98, Windows ME, Windows 2000 (Service Pack 2 or higher), Windows XP, Windows 2003] and linux (guess MAC users are out of luck for this one).

OpenOffice is one example of open source software. Much open source software is free and many are cross-platform, which means that there's a version for different operating systems (most readers here probably use some version of Windows but yes, there are other operating systems for the home user out there). 

To explore open-source software, check out http://sourceforge.net/


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## oldcoot (Jun 12, 2005)

If 5 lbs flour = 75 servings @ 1/4 cup ea, then (5 x 16) 80 oz / 75 = 1.07 oz per 1/4 cup.

So 1 lb. + 1 oz = 17 oz / 1.07 = 15.9 quarter cups or 4 cups Bread Flour.

Whee did I go wrong?

BTW: isn't "bread flour" made of wheat, too? Stuff I buy is! 

Just fooling around, I weighed four measured by the "standard" system of spooning it into the measuring cup, and then by sifting the flour onto a paper towel and gently pouring it into the cup. Came up with a whopping 10% difference in weight! A sufted 1/4 cup weighed a bare 1 oz, while the spooned 1/4 cup came in at 1.1+ oz.

Bt is all that really important? For example, changes in humidity can effect the weight greatly - depending upon how the flour is stored: an open bag?...a cannister with a loose lid?...Recently we use an SS cannister with an hermetically sealing lid (a present from a delightful young neighbor). The difference can be appreciable.

Still, since I simply estimate the quantities of everything in the white bread I bake, with essentially identical results each time, and toss all into the mixing bowl in random fashion before turning on the KA, I am unsure all this attention to detail is needed. I just adjust the consistency of the dough - if necessary - after a few minutes of mixing. Works for me.


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## Andy M. (Jun 12, 2005)

oldcoot said:
			
		

> If 5 lbs flour = 75 servings @ 1/4 cup ea, then (5 x 16) 80 oz / 75 = 1.07 oz per 1/4 cup.
> 
> So 1 lb. + 1 oz = 17 oz / 1.07 = 15.9 quarter cups or 4 cups Bread Flour.
> 
> Whee did I go wrong?


 
You didn't go wrong.  4 cups is the correct answer for bread flour.


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## oldcoot (Jun 12, 2005)

Oops - sorry - I thought it was 3 for Bread and 4 for wheat - had it backwards. Not unusual for me!

Anyway, that didn't require any involved math - which I never could fathom.  Just simple arithmetic.(Yeah, I used my on-screen calculator! )


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## Consul (Jun 13, 2005)

I just keep adding flour until I get the right feel to the dough. That works for making focaccia. 

Sorry I wasn't here in time for this one. My Internet access went away on a misunderstanding, and I only just now got it back.

The rule of thumb I follow is based on a conversion chart I found, that 4 ounces of flour equals one cup, as measured out using Michael's method above. So, dividing ounces by 4 should yield cups, in theory. This only applies to white flours (bread and all-purpose, and maybe cake), so the heavier flours will need different calculations.


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## Michael in FtW (Jun 15, 2005)

Consul - the problem with "the chart" is that it really doesn't really work for baking. While 4-oz/cup is about right for cake flour, all purpose is about 4.25-oz, and bread flour is a little over 5-oz. Someone somewhere mentioned a chart in "Baker's Illustrated" - published by the folks at "Cook's Illustrated" that I admire 2nd only to Alton Brown for TV shows ... but they are in the NorthEast - and didn't include Southern milled flours.

The "problem" didn't allow for using "charts" - it required you to figure it out from the information on the bag. That's why I used semolina flour data for the whole wheat flour.


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## oldcoot (Jun 15, 2005)

Mike, I'm not sure any weight per cup is of any real use, as too many factors affect the amount of flour in a measured cupful.

Obviously, the most precise recipe would give the weight, not the volume, of flour. With electronic kitchen scales so inexpensive now (mine was under $25), such might not be too exclusive. (Or both volume & weight could be noted?)

But then, with all the other variables present in bread making, even that would be no guarantee.


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## Consul (Jun 18, 2005)

I know the problem didn't allow for charts. I just told the way I go about it since the problem had been solved and explained already.

One of the things I learned in chemistry class was all about inaccuracy in measuring (which relates to significant digits). I think you'll find if you measure a dozen one-pound bags of the same flour using a nice, super-accurate scale that you'll get a wide variance of weights from bag to bag, maybe by as much as a three to four ounce range.

One of the things on my shopping list is a nice and accurate digital scale for the kitchen. I wouldn't mind getting some pipettes and a buret or two, either.  I'd also like one of those infrared thermometers (the kind that can tell you the temperature of a surface at a distance), but that's another post.


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