Maths Olympiad Prep

Library / /156 of 241

, 2021

Algebra Difficulty 2.3 Junior Find the answer Canada

In 12 years, Janice will be 8 times as old as she was 2 years ago. How old is Janice now?

Pick one

Solution

Suppose that Janice is xx years old now.

Two years ago, Janice was x2x-2 years old.

In 12 years, Janice will be x+12x+12 years old.

From the given information x+12=8(x2)x+12 = 8(x-2) and so x+12=8x16x + 12 = 8x - 16 which gives 7x=287x = 28 and so x=4x=4.

Checking, if Janice is 4 years old now, then 2 years ago, she was 2 years old and in 12 years she will be 16 years old; since 16=2×816 = 2 \times 8, this is correct.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.