Machine PizzaDate: 08/15/97 at 07:05:06 From: windows Subject: Pizza machine Hi! A machine for processing pizzas puts salami on top of every 18th pizza, adds pieces of pineapple to every 21st pizza, and adds peppers every 20th pizza. Since the machine started working, it has processed 100000 pizzas. 1. How many peppered pizzas with salami and pineapple has the machine processed? 2. How many peppered pizzas with salami but without pineapple has the machine processed? Thank you! Date: 08/20/97 at 16:07:37 From: Doctor Rob Subject: Re: Pizza machine I will assume that the first pizza with salami is the 18th, the first with pineapple is the 21st, and the first with peppers is the 20th. The actual answer will change if this is not so. Another easily envisioned start is if all three ingredients are added to the first pizza. The conditions do not say what starting scenario is used out of the 7560 possibilities. 1. [100000/L], where L is the least common multiple of 18, 21, and 20. This is because every L pizzas, all three ingredients are added. 2. [100000/18] - [100000/M], where M is the least common multiple of 18 and 21. This is because every 18 pizzas, salami is added, but every M pizzas, both salami and pineapple are added. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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