maths problem solving (counting?)

there are four quality inspectors inspecting boxes.

a batch of boxes is numbered in order from 1 to 2500. each inspector is inspecting 1 part

-Every 5th box has it's sticker inspected

-every 7th box has it's cardboard inspected

-Every 17th box has it's logo logo inspected

-Every 23rd box has it's packaging inspected

Q) Explain why no box is checked by all 4 inspectors

Q) Make a list of the numbers of all the boxes which are checked by 3 inspectors

I'm having a lot of trouble with this so your help will be appreciated! (Rofl) (Heart)

Re: maths problem solving (counting?)

Hello, ilikepizza!

Quote:

There are four quality inspectors inspecting boxes.

A batch of boxes is numbered in order from 1 to 2500. each inspector is inspecting one part.

. . Every 5th box has its sticker inspected.

. . Every 7th box has its cardboard inspected.

. . Every 17th box has its logo inspected.

. . Every 23rd box has its packaging inspected.

1) Explain why no box is checked by all four inspectors.

The box which is first inspected four times is numbered with the LCM of the four numbers.

. . $\displaystyle LCM(5,7,17,23) \:=\:5\cdot7\cdot17\cdot23 \:=\:10,\!465$

Hence, box #10,465 would be inspected four times.

. . But there are only 2,500 boxes.

Quote:

2) Make a list of the numbers of all the boxes which are checked by 3 inspectors.

$\displaystyle LCM(5,7,13) = 455$

Every 455th box would be inspected for its sticker, cardboard and logo.

These would be: #455, 910, 1365, 1820. 2275

$\displaystyle LCM(5,7,23) = 805$

Every 805th box would be inspected for its sticker, cardboard and packaging.

These would be: #805, 1610, 2415

$\displaystyle LCM(5,13,23) = 1495$

Every 1495th box would be inspected for its sticker, logo and packaging.

This would be: #1495

$\displaystyle LCM(7,13,23) = 2093$

Every 2093rd box would be inspected for its cardboard, logo and packaging.

This would be: #2093