Tsa 2016 q50

Rolls of a particular wallpaper have a repeating pattern every 60 cm of their length. Each roll is
10 m long and 50 cm wide. A wall 2.5 m high and 6.2 m wide is to be papered from ceiling to
floor with single lengths of paper hung vertically (drops).
How many rolls of wallpaper will be needed so that the pattern on each drop matches the next?
(No joins can be made in one vertical drop.)

A 3
B 4
C 5
D 6
E 7

I know that C is correct but WHY?
Please, help me! Thank you!

Reply 1

NamesAreEffort

So the wall is 620cm wide, and your drops are 50cm wide. 620/50 = 12.4, and as you can't use 2/5ths of a roll you've got 13 drops you have to use.

In terms of drop per roll, for the pattern to be the same, I have to cut bits off the end of every drop I make then make another from the "top" of every next pattern, otherwise the patterns will not be the same. Instead of it as a random pattern, imagine a rainbow pattern. If I want every colour to line up next to each other, I'd try to make them all start with red, and cut off the bottom of every "strip" to ensure they repeat over and over again.

So for a drop of 250cm high, I need 300cm worth of full "pattern" as 240cm is not enough, and nothing in between is a multiple of 60 which I need as I want to maintain full patterns to line up to each other, because then I would manually cut off the very bottom 50cm.

If I need 300cm worth of full pattern for a drop, that means out of a roll of 10m (1000cm), I can get 3 full drops. If I have 13 drops, and I can get 3 drops per roll, then I need 13/3 rolls, which is 4 and a third. Obviously if I were buying rolls for example, I wouldn't be able to buy 1/3rd of a roll, so I would buy 5, and I would make drops from each of them.

So in total I need 5 rolls. C.

(edited 6 years ago)