UKMT Cayley Olympiad, 2017

Number theory Difficulty 2.0 Junior Prove it United Kingdom

Peaches spends exactly £3.92 on some fruit, choosing from apples costing 20p each and pears costing 28p each. How many of each type of fruit might she have bought?

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.