Maths Olympiad Prep

Library / /145 of 520

Algebra Difficulty 5.3 AIME, harder Find the answer

71. One day, at the entrance of the China Pavilion at the Shanghai World Expo, 945 visitors had already begun waiting to enter. At this time, several people were still coming to the entrance every minute to prepare for entry. In this way, if 4 ticket-checking gates were opened, all waiting visitors could enter in 15 minutes; if 8 ticket-checking gates were opened, all waiting visitors could enter in 7 minutes. Now, it is required that all waiting visitors can enter within 5 minutes, and \qquad ticket-checking gates need to be opened.

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

Solution

Reference answer: 11

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: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.