My friend, Neville, sometimes finds mathematics a little tricky.

I recently asked him to buy me some ribbon for my daughter's pretty pink bonnet.

He went to the haberdashery shop for the required length but he accidentally interchanged the feet and inches when asking.

When I measured the resulting ribbon I only had 30% of the length I required.

How much ribbon did I originally ask for?

Puzzle Copyright © Kevin Stone

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Hint

Remember that there are 12 inches in a foot.

Answer

I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).

I asked him to buy me A feet and B inches, which is a total of 12A + B inches. Neville accidentally bought me B feet and A inches, which is 12B + A.

We know that 12B + A is actually only 30% of what we wanted, so:

12B + A = 0.3 x (12A + B)

Multiply throughout by 10:

120B + 10A = 3 x (12A + B)

120B + 10A = 36A + 3B

117B = 26A

The first number where this gives a sensible answer is when A = 9, and B = 2.