First convert your values to Plato as SG isn’t linear for mass of sugar in a volume vs gravity points. This allows you to use simple algebra to average different beers. If the two gravities are very close then not converting will mean you will be off by only a few points, but if the gravities are vastly different your calculated value will be off by quite a bit.
Multiply your starter volume and wort volume by their original Plato gravities respectively to produce numbers that can be combined to derive an average gravity reading from the blend.
Do this by dividing the sum of the gravity-volume products by the sum of all wort:
( ( OG1 * V1 ) + ( OG2 * V2 ) ) / ( V1 + V2 ) = SG
- OG1 is the original gravity of your starter wort in Plato
- V1 is the volume of your starter wort
- OG2 is the original gravity of your wort in Plato
- V2 is the volume of your wort
- SG is the specific gravity of the blend in Plato
At the end convert back to SG from Plato using an appropriate table or online calculator.
If blending more than two parts:
( ( OG1 * V1 ) + ( OG2 * V2 ) [ + ( OGn * Vn ) ] ) / ( V1 + V2 [ + Vn ] ) = SG
In this case:
( ( 1.040 * 0.25 ) + ( 1.076 * 5 ) ) / ( 0.25 + 5 ) =
( 0.26 + 5.38 ) / 5.25 =
5.64 / 5.25 =
1.074 specific gravity of blended starter and wort
Kudos to @jsled and @tobias-patton for providing the clues to solve this problem