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Match one underlying and one terminal strike amount
At expiry, underlying plus put gives S+max(K−S,0). Call plus a certain K gives max(S−K,0)+K. Both equal max(S,K). The strike-funded leg is a terminal amount, not K paid again today.
Discount the terminal cash leg
D is the current discount factor for certain cash due at the same expiry. The current cost of terminal K is KD. The selected price equality uses same-underlying, same-strike, same-expiry European options and no intervening underlying income or benefit.
This is a current-value relationship under compatible contract and financing assumptions.
Recover a missing price on the stated basis
With S0 = 100, K = 100, D = 0.95 and C0 = 8, the implied put is 8+95−100 = 3. This is a consistency calculation, not a model that separately estimates all option-pricing inputs.
Avoid an unqualified extension
American exercise opportunities, dividends, different strikes, mismatched expiries or transaction frictions require their own treatment. A discrepancy in entered quotes does not by itself identify an executable transaction.