Posted by **Linda** on Wednesday, January 25, 2012 at 8:28am.

John checks every 8th item for color, and Colin checks every 12th item for durability. If 1,920 items passed by both of them, how many items were checked by both John and colin?

How do I figure this?

- math -
**Reiny**, Wednesday, January 25, 2012 at 9:36am
1920/12 = 160

1920/8 = 240

Can you do anything with that?

- math -
**Linda**, Wednesday, January 25, 2012 at 9:55am
still confused! do they want to know how many items were checked by BOTH john and calvin, meaning the same item?

- math -
**Reiny**, Wednesday, January 25, 2012 at 10:18am
John checks items

#8 #16 #24 #32 #40 .... #1920

the 8 means he checks item #8 , not 8 items

so isn't the above just like the times table for 8 ?

how many entries are there to get to 1920 ?

that would be 1920/8 or 160

So John had to check 160 items and that last item would be item # 1920.

Use the same argument for Colin.

So John checked 160 items and Colin checked 240 items

So number of items checked by BOTH John AND Colin = 400

(I assumed that they were not looking at the same items, if they are checking the same line , then we have to subtract all common items from the total.

A slightly more difficult question, but ...

what numbers would be divisible by both 8 and 24 ? )

- math -
**Linda**, Wednesday, January 25, 2012 at 10:48am
Its a multible choice question and the choices are 20,40,60,80 and I still don't see how to come up with any of these answers

- Correction -math -
**Reiny**, Wednesday, January 25, 2012 at 12:23pm
You are right, I should have taken the intersection of the two sets, I mis-read the question

so we are looking for numbers which are both divisible by 8 and by 12

the smallest of these would be the LCM of 8 and 12 which is 24

so the 24th is checked by both, the 48th is checked by both, etc

then 1920/24 = 80

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