How much ribbon?

[mobilemu]

Julian went to buy some ribbon for my bonnet. He went to the shop for the required length but interchanged the feet and inches. When i measured the resulting ribbon I only had 30% of the length i required. How much ribbon did I originally ask for?

[mohill]

9ft 2in

Suppose you wanted a length of x ft + y in
That would be (12x + y) in
Instead you received y ft + x in
That would be (12y + x) in

12y + x = 3/10 of(12x + y)
ie 10(12x + y) = 3(12y + x)
120x + 10y = 36x + 3y
117y = 26x
(Divide by common factor 13)
9y = 2x
The simplest numbers that would make this true are
y =2 and x = 9

So you wanted 9ft 2in and received 2ft 9in

[mohill]

sorry mobilemu
I have got my working mixed up part way down.
It should have read:
12y + x = 3/10(12x + y)
10(12y + x) = 3(12x + y)
120y + 10x = 36x + 3y
117y = 26x
Divide by common factor 13
9y = 2x
The simplest solution to this is x = 9 and y = 2

So you wanted 9ft 2in and received 2ft9in
Cheers