On a linear X temperature scale, water freezes at $-121\mathrm{.}0$X and boils at $401\mathrm{.}0$X$.$ On a linear Y temperature scale, water freezes at $-73\mathrm{.}00$Y and boils at $-38\mathrm{.}00$Y$.$ A temperature of $40\mathrm{.}00$Y corresponds to what temperature on the X scale?