No, the upper cable has 180,000 lb, and each of the two lower cables has 90,000 lb - so combined, the two lower cables total 180,000lb. The sum of the vertical forces at the connection between the 2 lower cables to the 1 upper cable must = zero.
No, the scale does NOT measure half the force, it is measuring the only force that is applied to the system - 25 lb - that is in static equilibrium.
==> So you are not believing my math, and my graphics was not intuitive to you, so lets try this:
EXPERIMENTAL PROOF: The foundation upon which scientific theory is proven.
I used my DILLON tension gauge and a setup that mimics your 'scrap yard scale' pictorial:
First, measured the mass of the 2 x 25 lb weights to verify that they are indeed 50 lb total - measured in the vertical direction, using the DILLON gauge.
Photographic proof: A little hard to read in this photo, but it states 50 lbf. But I have other photos I can share if you need further proof. And the weights are stamped with 25lb - and they have been checked from the USPS scale because I use them to calibrate my bicycle power meter.
Attachment 1730130
Next, I applied 2 x 25lb masses to each end of a horizontal beam with end pulleys attached, connected via ropes (different color ropes to show that there is no 'sleight-of-hand'), with a centrally placed DILLON tension gauge (the same one I used to verify the 50 lb weights).
Photographic proof:
Attachment 1730131
Then read the DILLON tension gauge:
Photographic proof:
Attachment 1730132
And low and behold, the gauge read 50 lbf.
Exactly what static equilibrium states.
So, all is good, the earth still spins on its axis, the sun will shine tomorrow, William McCormack is a believer in science, and I do NOT need to get a refund on my engineering degree. Life is good!