I recently asked a friend of mine to buy me some ribbon for my latest embroidery project.

He went to the haberdashery shop for a particular length, but he accidentally interchanged the feet and inches.

When I measured the purchased 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).

Reasoning

I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.

He accidentally bought me B feet and A inches, which is 12B + A inches.

We know that 12B + A is actually only 30% of what I 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

B = 26A ÷ 117

Don't forget that A and B can only be integers, and between 0 and 11.

Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.

5 x 26 = 130

6 x 26 = 156

7 x 26 = 182

8 x 26 = 208

9 x 26 = 234 (*)

10 x 26 = 260

11 x 26 = 286

The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.

So, I originally asked for 9 feet 2 inches.