1. ## sequences

A machine for making donuts produces plain donuts. It then puts chocolate coating on top of every 24th donut, fills every 30th donut with strawberry jam and covers evry 45th donut with sprinkles. Sine the machines started working, it has processed 25000 donuts.

a/ How many chocolate coated donuts with jam and sprinkles has the machine produced?

b/ How many donuts with jam that are either chocolate coated without sprinkles or with sprinkles but without chocolate coating, has the machine produced?

A machine for making donuts produces plain donuts. It then puts chocolate coating on top of every 24th donut, fills every 30th donut with strawberry jam and covers evry 45th donut with sprinkles. Sine the machines started working, it has processed 25000 donuts.

a/ How many chocolate coated donuts with jam and sprinkles has the machine produced?
lcm(24,30,45) = 360, so every 360th donut has all three extras.

b/ How many donuts with jam that are either chocolate coated without sprinkles or with sprinkles but without chocolate coating, has the machine produced?
donuts with jam and sprinkles only: lcm(30,45) = 90, every 90th donut but leave out every 360th donut (since it will also have chocolate)

donuts with jam and chocolate only: lcm(24,30) = 120, every 120th donut but leave out every 360th donut (since it will also have chocolate)

btw there are no donuts with chocolate and sprinkles only, although those are my favorites. :-(

Hope this helps.

3. ## Thanks for the help

Thanks for the help, I understand it now