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Pizza Problem
By Isabelle Soh on Saturday, July 28, 2001 - 05:36 am:

Hi guys,

Here's a problem which will challenge:

A machine for processing pizzas puts salami on the top of every 18th pizza, adds pieces of pineapple to every 21st pizza and peppers every 20th pizza. Since the machine started working, it has processed 100000 pizzas.

(a) How many peppered pizzas with salami and pineapple has the machine processed?

(b) How many peppered pizzas with salami but without pineapple has the machine processed?

Please include a solution and method.

Yours sincerely,
Isy

By David Lee on Friday, September 07, 2001 - 05:18 pm:

(a) All 3 toppings occur on multiples of the LCM of 18, 20 and 21
18=2x3x3
20=2x2x5
21=3x7
therefore LCM=2x2x3x3x5x7=1260
100000/1260 = 79.4 so 79 pizzas have all 3 toppings

(b) pizza with just pepper and salami=
{all pizzas with peppers and salami}-
{pizzas with all 3 toppings}

LCM of 18 and 20=2x2x3x3x5=180
100000/180=555.6 .... 555 pizzas with salami and pepper (and maybe some pineapple)

Answer = 555 - 79 = 476

By The Editor

Can you now work out how many pizzas will have each of the other combinations of toppings?