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