Aproduct is currently priced at $10. if it is discounted by 10%, the profit margin
will be 10%. what is the cost of the product?

Either $8.18 or $8.10 -

Take %10 off of $10, and we are left with $9.

Now, we know that you are going to make a profit of %10 of whatever the cost was. Let x be the cost of the product. The cost of the product plus your profit margin must equal 9. Therefore:

x + 0.10x = 9

1.1x = 9

x = 8.18

The only thing is, I'm not sure if a profit margin of ten percent means you receive %10 of the cost (in which case this answer is correct), or %10 of the $9 (in which case the cost is $8.10). It's more a case of wording than math.

But if I had to, I'd answer $8.18. Maybe someone else can confirm.