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But this sounds like real life, so I'll just answer.

Let's take your first example, and then generalize.

You have 12.5% SH, so x gallons contain 0.125x of SH. You want 50 gallons total, of which 1% (.01*50 = 0.5 gal) is SH. So you want 0.125x = 0.5.

Solving, x = 0.5/0.125 = 4 gallons. The remaining 50 - 4 = 46 gallons will be water.

As a formula, we see that 0.5 was the desired gallons (50) times the desired concentration (1%), and the 0.125 was the provided concentration. So the formula you want is

Gallons to use = Desired gallons*Desired concentration/Provided concentration.

Trying this out on the second example, we get 30*0.06/0.125 = 14.4, so you'd use 14.4 gallons in 30 - 14.4 = 15.6 gallons of water. Checking, you're using 0.125*14.4 = 1.8 gallons of pure SH, and 1.8/30 = 0.06, the correct concentration.