Charu's quiz scores

Charu plays three rounds of a quiz. Her scores: 7p − 3q, 8p − 4q and 6p − 2q. Here p is the marks for a right answer and q the penalty for a wrong one.

So in round 1 she got 7 right and 3 wrong; round 2, 8 right and 4 wrong; round 3, 6 right and 2 wrong. The letters let us write each score before we even know the marking scheme.

If a right answer gets 4 and a wrong one loses 1 (p = 4, q = 1), round 1 is 7 × 4 − 3 × 1 = 28 − 3 = 25. (With no penalty, q would be 0.)

Her total: (7p − 3q) + (8p − 4q) + (6p − 2q). Remove the brackets (they have + in front, so nothing changes), then group like terms:

(7p + 8p + 6p) + (−3q − 4q − 2q) = 21p − 9q.

Her friend Krishita scored 23p − 7q. Who did better? Krishita got more right and fewer wrong, so Krishita. By how much? (23p − 7q) − (21p − 9q) = 23p − 7q − 21p + 9q = 2p + 2q.