Library / UKMT Senior Mathematical Challenge /175 of 212

UKMT Senior Mathematical Challenge, 2019

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The numbers $x$ , $y$ and $z$ satisfy the equations $9x+3y-5z=-4$ and $5x+2y-2z=13$ . What is the mean of $x$ , $y$ and $z$ ?

(A) $10$ (B) $11$ (C) $12$ (D) $13$ (E) $14$

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.