The passage, when transposed 3½ tones up, will be in the key of

The passage is written in C major (no sharps or flats in the key signature). Transposing 3½ tones up means moving every note up by 7 semitones, which is equivalent to a perfect fifth.

Starting from C and counting up 7 semitones: C → C♯ → D → D♯ → E → F → F♯ → G. The new tonic is G, so the passage will be in the key of G major (one sharp, F♯).

A useful shortcut: transposing up by a perfect fifth from any major key adds one sharp (or removes one flat) to the key signature. C major (no sharps) becomes G major (one sharp).