The payoff a player will win by opening the winning box on their $k$th try is $$ \text{Payoff}(k) = 100 - kx. $$ The player will open the winning box on their $k$th try with probability of $\frac{1}{4}$. The expected payoff is therefore $$ \text{E}[\text{Payoff}] = \frac{1}{4} \sum_{k=1}^{4} (100 - kx). $$ If the game is fair, the expected payoff should equal zero. $$ \frac{1}{4} \sum_{k=1}^{4} (100 - kx) = 0 $$ $$ 400 = x \sum_{k=1}^{4} k $$ $$ 400 = 10x $$ $$ x = 40 $$ This result makes sense, as the player will on average open the winning box after opening 2.5 boxes, and $\frac{100}{2.5} = 40$.