ATC CONFUSION REF ASSIGNED ALT.

Narrative

CLBING THROUGH FL200 ON SLC ATC (128.55) WE WERE CLRED TO FL350. COPLT READ BACK CLRNC TO ATC AND SINCE WE FILED FOR FL310 HE THEN ASKED ME IF FL350 WAS OK. I CHKED OUR PERFORMANCE DATA COMPUTER AND IT SHOWED FL340 AS OUR OPTIMUM ALT SO I SAID TO HIM THAT WE WOULD TAKE IT (FL350). COPLT CHKING IN WITH NEXT CTLR (132.55); 'ACR X CLBING TO FL350.' CTR ACKNOWLEDGED WITH; 'ROGER ACR X.' AS WE WERE CLBING THROUGH FL317 THE CTLR SAID; 'ACR X I HAVE YOU AT THIRTY-ONE SEVEN.' THE COPLT ACKNOWLEDGED SAYING; 'ROGER; WE'RE CLBING TO FL350.' CTR THEN SAID; I HAVE YOU FILED AT FL310. THE COPLT EXPLAINED THAT THE PREVIOUS CTLR HAD CLRED US TO FL350 AND WE ACCEPTED IT BUT WOULD GO BACK TO FL310 IF REQUIRED. ATC SAID NO; CONTINUE TO FL350. I THEN RE-EXPLAINED THE SITUATION TO ATC AND NO FURTHER DIFFICULTIES WERE EXPERIENCED. THE COPLT SUGGESTED TO THE CTLR THAT SHE CONTACT THE PREVIOUS CTLR BUT SHE SAID HE HAD ALREADY LEFT WORK. SHE ALSO SAID SHE SHOULD HAVE CONNECTED WHAT SHE HEARD WITH WHAT SHE SAW. TFC WAS LIGHT.