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.



Let required length = x feet y inch = (12x+y) inch
he brought = y feet x inch = (12y+x) inch

12y+x= \frac{5}{8}(12x+y)\\ \\8( 12y+x)= 5(12x+y)\\ \\ 96y+8x=60x+5y\\ \\91y=52x\\ \\y= \frac{52}{91}x=\frac{4}{7}x

y is less than 12.(because if we have 12 inch, it will be counted as 1 foot)
Since he interchanged feet and inch, he even x should be less than 12.

So, only option satisfying is x=7, y = 4
So i had asked for 7 feet 4 inch of ribbon