Math Help Please

Discussion in 'Professional Chefs' started by frizbee, Jan 11, 2011.

  1. frizbee

    frizbee

    Messages:
    187
    Likes Received:
    10
    Exp:
    Professional Chef
    I have a new food item being used and it calls for egg whites to be added at 30% of the total volume.

    The liquid egg bags I have are 5 gal/20# bags. The egg whites are 2#/ 1 qt containers.

    So how much egg white do I add to a whole bag of easy eggs to achieve 30% of the volume? And what would the formula be to figure this out for the future..

    Thanks Chefs! I always appreciate your help!

    Frizbee 
     
  2. kuan

    kuan Moderator Staff Member

    Messages:
    6,802
    Likes Received:
    383
    Exp:
    Retired Chef
    5 gallon x 30/100 = 1.5 gallons or 6 qts.
     
  3. frizbee

    frizbee

    Messages:
    187
    Likes Received:
    10
    Exp:
    Professional Chef
    Awesome Kuan! Thanks
     
  4. petemccracken

    petemccracken

    Messages:
    3,401
    Likes Received:
    160
    Exp:
    Professional Chef
    Something seems strange, from the sources I've found, 4 cups (1 quart) of liquid whole eggs weighs about 34.286 ounces or 2 pounds 2 1/4 ounces. Therefore, 5 gallons (20 quarts) would weigh about 42 pounds 13 3/4 ounces, not 20 pounds as you indicate, maybe it is 20 kilograms? The weight of egg whites seems very close.

    Total volume = V
    Volume of liquid eggs = L
    Volume of egg white = W

    If the recipe calls for 30% of the TOTAL VOLUME to be egg whites, then V = L + W and  %W =( W/V)*100 = (W/(L+W))*100 = 30%

    So, dividing both sides by 100 : W/(L+W) = 0.3

    Multiplying both sides by (L+W): W=0.3(L+W) = 0.3L+0.3W

    Subtracting 0.3W from both sides : W-0.3W = 0.3L or  0.7W=0.3L

    Dividing both sides by 0.3: 0.7W/0.3=0.3L/0.3 or 2.3333W=L

    Dividing both sides by 2.3333: W = 0.42857755L

    What the h3ll does this mean? For every 5 gallon (20 quarts) bag of liquid eggs, use 8.57155 quarts (8 quarts, 18.29 ounces) of egg whites or 8 quarts + 2 cups + 2 ounces + 1 teaspoon + 3/4 teaspoon of egg whites.

    8.57155 quarts of egg whites divided by the total volume of 28.57155 quarts = 0.30 = 30%
    I'd probably use 8 1/2 quarts of whites per 5 gallons of liquid eggs.

    I'd certainly check the weight of 5 gallons of liquid eggs before proceeding.
     
  5. petemccracken

    petemccracken

    Messages:
    3,401
    Likes Received:
    160
    Exp:
    Professional Chef
    The OP said it was 30% of the Total volume, not 30% of the volume of liquid eggs.
     
    If it is really 30$ of the liquid egg volume, KUAN is correct.
     
  6. cheflayne

    cheflayne

    Messages:
    4,171
    Likes Received:
    536
    Exp:
    Professional Chef
    The original answer didn't state whether it was to liquid eggs or not, so you could still use the formula either way you desire. Add 1.5 gallon white to 5 gallon liquid egg; or add 1.5 gallon white to 3.5 gallon liquid egg to equal 5 gallon. While the results will be decidedly different, the formula is still correct.

    I am going to go out on a limb here and suggest that the answer to the original question would be 6 bags of whites to 1 bag of liquid egg. My logic on that answer is that the resulting product use is complete with no leftover partials.
     
    Last edited: Jan 11, 2011
  7. kuan

    kuan Moderator Staff Member

    Messages:
    6,802
    Likes Received:
    383
    Exp:
    Retired Chef
    Oh OK.  The other scenario is the liquid eggs represents 70% of the total volume and the eggwhites reprents 30%.  So the ratio is 3:7.

    So 5 gallons divide by 7 and multiply by 3

    In short (5/7)x3=2.14 gallons of eggwhite.

    But I agree with cheflayne.  It seems the easiest.
     
  8. petemccracken

    petemccracken

    Messages:
    3,401
    Likes Received:
    160
    Exp:
    Professional Chef
    Hm, (5/7)*3 = 0.714285*3 = 2.142857 gallons*4 = 8.57142857  /img/vbsmilies/smilies/crazy.gif, pretty close, no?
     
    Last edited: Jan 11, 2011
  9. kuan

    kuan Moderator Staff Member

    Messages:
    6,802
    Likes Received:
    383
    Exp:
    Retired Chef

    Heh yeah  /img/vbsmilies/smilies/lol.gif