Here’s the CORRECT way to do the problem…

Okay… here’s what you know…

Michael LOST 60% (which means that he only got back 40% of the original price of the book)

Sally GAINED 10% (which means that she sold the book for 110% of the price that she paid for the book… 100% to get HER full price back and then an ADDITIONAL 10% to MAKE a 10% profit)

and Mary paid $22….

Okay… starting with Sally gained 10%… so $22 is 110% of what?

$22 = 110% of x

$22 = 110% * x

x = $22/110 = $20

Now Michael LOST 60%…

so $20 is 40% of what?

$20 = 40% of y

$20 = 40% * y

y = $20/40% = $50

Michael paid $50 dollars for the book

_________________

Checking your work…

Michael paid $50 for the book…

He sold it to Sally at a loss of 60%…. that means that he sold it to Sally for 40% of the price he paid… or $50 x 40% = $20

Now Sally sold the the $20 book and MADE 10%…. so what is 110% of $20? $20 x 110% = $22

Michel sold to Sally at 32 / 1.6 = $20

Sally sold to Mary at 20*1.1 = $22

easy

S = 0.4 * O

M = 1.1 * S

M= 22

Work those and you should get O (original price) fairly quickly.