Competition problem — Algebra — Maths Olympiad Prep

Library / /6 of 94

Algebra Difficulty 4.0 AIME Find the answer United States

Problem:

There are some red and blue marbles in a box. We are told that there are twelve more red marbles than blue marbles, and we experimentally determine that when we pick a marble randomly we get a blue marble one quarter of the time. How many marbles are there in the box?

Your answer

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

Solution

Solution:

Call the number of blue marbles $x$ , so the number of red marbles is $x + 12$ and the total number of marbles is $2x + 12$ . The probability of picking a blue marble is $\frac{x}{2x + 12} = \frac{1}{4}$ . Solving, $x = 6$ , so $2x + 12 = 24$ .

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.