Solve 2-D Spring Problem: 21.75 & 22.25 Equations

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The discussion centers on solving a 2-D spring problem using two equations related to spring compression, with the total weight on the spring calculated at 31.25 lb. The spring constant, k, is assumed to be 5 lb/in, leading to a calculated displacement of 0.6 inches. The maximum spring compression is determined to be 6.25 inches, leaving 6.75 inches for height after accounting for the spring's original length of 13 inches. Calibration adjustments are suggested to ensure accurate measurements, and it's important to verify that the selected spring can handle the required compression without bottoming out. The calculations emphasize the need for careful consideration of spring properties in practical applications.
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http://i.imgur.com/uKydC.png

Here is the problem. I came up with two equations:

Upper Lc: 21.75=k(Lo-Lcu)
Lower Lc: 22.25=k(Lo-Lcl)

I am not sure what to do with this? How do I figure this out?
 
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Total weight on spring = 8 + 22 + scale platform + .25 . If you use 1 lb for the platform then total = 31.25 lb. Assuming k = 5 lb/in then d = (.25 + .25) / 5 + .5 = .6 inches. Max spring compression would be 31.25 / 5 = 6.25 inches. Starting with a 13 in. long spring leaves 6.75 for h. I would expect you would need to plan some adjustment for calibration. This also assumes the chosen spring can be compressed the needed amount without bottoming out.
 

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