Rachel pays $131.44 for a desk, including tax. The tax is 31 cents less than 1/16 the desk's price. What is the price for the desk before adding the tax?
Let X be the price for the desk before adding the tax.
The tax is (X/16) - $0.31
So the desk price including tax is X + (X/16) - $0.31 = $131.44
Multiplying through the parentheses gives X + X/16 - $0.31 = $131.44
Subtracting X from both sides gives X/16 - $0.31 = $131.44 - X
Adding $0.31 to both sides gives X/16 = $131.75 - X
Adding X to both sides gives X + X/16 = $131.75
Multiplying through the parentheses gives 16X + X = $2108
Combining like terms gives 17X = $2108
Dividing both sides by 17 gives X = $124
The price of the desk before adding the tax is $<<124=124>>124. Answer: \boxed{124}.