The input voltage, Vo, varies from 50 x 100 mV/psi = 5 V at 50 psi to 150 x 100 mV/psi = 15 V at 150 PSI. Since you want the output, Vout, to vary from 0 to 2.5 V, the range of the input signal, which is 10 V (V150 psi - V50psi), must be attenuated by a factor of 2.5/10 = 0.25 and then the input signal must be offset to zero at 50 psi.
The first op-amp is wired as a unity-gain inverter, meaning Vx varies from -5 V to -15 V over the 50 psi to 150 psi range as Vo varies from +5 V to +15 V over that range. The second op-amp stage is wired as an inverting summing amplifier with a gain of Ry/R = 625/2500 = 0.25 for each of the two inputs, Vref and Vx. Thus when the input is at +5 V, Vx = -5 V and when this is summed with Vref = +5 V the result is Vout = 0. When the input is at +15 V, Vx = -15 V and when this is summed with Vref = +5 V and the difference multiplied by the gain of 0.25 and inverted the result is Vout = +2.5 V.
Note that the first op-amp must be capable of a negative output of -15 V and the second op-amp must be capable of a positive output of only +2.5 V. Normally you would use a pair of dual op-amps with ±15 VDC power rails, each op-amp capable of ±15 V full-scale output. This is not common (rail-to-rail output). Most op-amps with ±15 V supplies will only swing their outputs ±10 V. This can be accommodated by decreasing the gain of the first stage, making the feedback resistor, Rx, smaller to limit the output Vx to -10 V at 150 psi. You will then have to adjust the resistor values in the second stage to restore the 0 V to +2.5 V output range. I will leave those calculations to you now that I have explained the principle..
Is this a homework problem for use in a class you are taking?
