Maths Olympiad Prep

Library / /10 of 80

Algebra Difficulty 4.0 AMC 10/12 Find the answer North Macedonia

The book that Marko reads has 242242 pages. The first day he has read 2222 pages. During the second day he has read 44 pages more than the first and the same during the third day. How many days will Marko need to finish the book if he reads two pages more than the third day each day from the fourth day onward?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Let xx be the number of days from the fourth day onward that Marko needs to finish the book. Then we have the equation
22+2⋅(22+4)+x⋅(22+4+2)=242, 22 + 2 \cdot (22 + 4) + x \cdot (22 + 4 + 2) = 242,
from where we obtain x=6x = 6. So Marko will read the book for 3+x=3+6=93 + x = 3 + 6 = 9 days.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.