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Puzzle Details

My friend, Alex, struggles a little. 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 accidentally interchanged the feet and inches.

When I measured the resulting ribbon I only had 5÷8 of the length I required.

How much ribbon did I originally ask for?

Remember that there are 12 inches in each foot.

I asked for 7 feet, 4 inches and my friend brought me 4 feet, 7 inches.

If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:

(5 ÷ 8) x (12 x A + B) = (12 x B + A)

Simplifying gives:

A = (91 ÷ 52) x B

As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet. B = 4 is the only possible value, which means that A = 7. So I originally asked for 7 feet, 4 inches. QED.

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