Any slider in the Red channel can only affect the R value of your output pixel. Likewise, any slider in the Green channel can only affect the G value of the output pixel, and any slider in the Blue channel can only affect the B value of the output pixel.
Your input values are R50 G200 B10
Normally
the Red channel sliders are R100 G0 B0 this means 100% of 50 + 0% of 200 + 0% of 10. Output R=50
the Green channel sliders are R0 G100 B0 this means 0% of 50 + 100% of 200 + 0% of 10. Output G=200
the Blue channel sliders are R0 G0 B100 this means 0% of 50 + 0% of 200 + 100% of 10. Output B=10
so your output pixel = R50 G200 B10 = input values = unchanged
Lets change the red channel sliders only, remember this can only affect the R value of the output pixel.
Red channels sliders are now R0 G0 B100 this means 0% of 50 + 0% of 200 + 100% of 10. Output R=10
Green channel sliders are R0 G100 B0 this means 0% of 50 + 100% of 200 + 0% of 10. Output G=200
Blue channel sliders are R0 G0 B100 this means 0% of 50 + 0% of 200 + 100% of 10. Output B=10
so your output pixel = R10 G200 B10
Lets change the R channel some more.
Red channels sliders are now R0 G50 B100 this means 0% of 50 + 50% of 200 + 100% of 10. Output R=110
Green channel sliders are R0 G100 B0 this means 0% of 50 + 100% of 200 + 0% of 10. Output G=200
Blue channel sliders are R0 G0 B100 this means 0% of 50 + 0% of 200 + 100% of 10. Output B=10
so your output pixel = R110 G200 B10
Why would adjusting the Blue slider of the Red channel make blues purple?
Input R0 G0 B255 = pure blue
Red channel sliders R100 G0 B100 which means 100% of 0 + 0% of 0 + 100% of 255. Output R=255
Green channel sliders R0 G100 B0 which means 0% of 0 + 100% of 0 + 0% of 255. Output G=0
Blue channel sliders R0 G0 B100 which means 0% of 0 + 0% of 0 + 100% of 255. Output B=255
Output pixel = R255 G0 B255 = pure magenta
HTH
James
Edit: And Pat beat me to it, with pictures and everything 
and this was my first real post too.