Maths Olympiad Prep

Track / Stage 4 / 196 of 340 #456 of 1964

Problem 456

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

1. Option 1. To a confectionery factory for cake packaging, 5 rolls of ribbon, each 60 m long, were delivered. How many cuts need to be made to get pieces of ribbon, each 1 m 50 cm long?

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Answer: 195.

Solution: From one roll, 40 pieces of ribbon, each 1 m 50 cm long, can be obtained. For this, 39 cuts are needed. Therefore, a total of 539=1955 \cdot 39=195 cuts are required.

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