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posted by AMI on .
I HAVE $100.00
THE GST IS 10%
THEREFORE TO GET THE GST PORTION I DO THE FOLLOWING: 100/11=9.09
NOW
I HAVE $100.00
THE GST IS 15%
THEREFORE 100/? =13.04

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What is GST? 
I presume this is a tax, probably Goods and Services Tax in Canada. Your post isn't clear. If you have 100 to spend on an item it will cost you 100 + 10% of 100. Or you may mean that the total cost of an item, including GST, is 100.00. And you want to know the cost without GST?

Goods and Services Tax (applies to all Canada). Some provinces combine with the provincial sales tax to call it Harmonized Sales Tax (HST).
Assume $100 includes GST, then the GST portion is $100*(10/110)=$100/11.
If the GST rate is 15%, then the GST portion will be $100*(15/115).