I need help finding out how did the authors got the values R1 = 30.45kΩ and R2 = 19.55kΩ.

When I for solve for R1 and R2 I get the following values:
R1 = 30.440kΩ
R2 = 19.560kΩ

Equation I used was:
R2*(2.5V)/(50000Ω) = 0.978V

Please help me with this.

 

So the discrepancy is 10Ω or 0.05%. Don't worry about it.

 

Thank you for your prompt assistance. But surely this discrepancy can't be correct because if you check the continuing example in the attachment, you would see the authors get an R1 = 1.45kΩ and R2 = 3.55kΩ.

If I calculate using the same equation as before but now with 5kΩ I would get R1 = 2.556kΩ and R2 = 2.444kΩ.

Equation I used was:
R2*(2.5V)/(5000Ω) = 1.278V

 

For Vx = 1.278V and R1 +R2 = 5K the correct solution is R1 -> 2.444K R2 -> 2.556k
But can you buy 2.444K or 2.556 resistor ?

 

Thanks for your input Jony130. That is the value I got but apparently the authors got different R1 and R2 values for both of these examples. The first example differed only slightly while the second example is by a landslide.

 

Don't worry too much about it. Error in printing can happen.

 

I hope that is the case. Thanks for your time.