Math Help Please

[frizbee]

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 

 

[kuan]

5 gallon x 30/100 = 1.5 gallons or 6 qts.

 

[frizbee]

Awesome Kuan! Thanks

 

[petemccracken]

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.

 

[petemccracken]

The OP said it was 30% of the Total volume, not 30% of the volume of liquid eggs.
 

5 gallon x 30/100 = 1.5 gallons or 6 qts.

If it is really 30$ of the liquid egg volume, KUAN is correct.

 

[cheflayne]

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.

 

[kuan]

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.

 

[petemccracken]

Hm, (5/7)*3 = 0.714285*3 = 2.142857 gallons*4 = 8.57142857  /img/vbsmilies/smilies/crazy.gif, pretty close, no?

 

[kuan]

Hm, (5/7)*3 = 0.714285*3 = 2.142857 gallons*4 = 8.57142857  /img/vbsmilies/smilies/crazy.gif, pretty close, no?

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