Equation needed for Additional wort.

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The problem:
What is my new O.G???
Tried to locate an equation. But found no clear accepted equation.

My Barley Wine was too dry. So I remashed at 158, and added 1 more gallon of high gravity wort to a beer that finished primary fermentation.
Here is my list of current known data:

OG1 = 1.115
FG1 = 1.004
Volume = 4.1 gallons

OG2 = 1.100
FG2 = N/A
Volume = 1gallon

Total new volume - 5.1 gallons.

Also, for the O.G. Do I need to take an average of my O.G. + my Yeast starter batch of 2quarts?

Thanks lads.

 

[kanzimonson]

Did you pitch a lot of liquid from the starter or did you decant? If it's a cup then let's just ignore it.

So for the first batch: 4.1 x 115 = 471.5 gravity points
For the second: 1 x 100 = 100 gravity points

571.5 gravity divided by 5.1 gal = 112

Your theoretical OG of combining these two batches is 1.112

 

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Thanks!
So, only if you add pure DME or suger will the OG go up?

 

[kanzimonson]

Remember, OG is a measure of density. Sugar per volume. You have to increase the sugar content more than you increase the volume to make the OG go up.