   SEARCH HOME Math Central Quandaries & Queries  Question from janet: Hello I need to figure what one would pay pst 8% gst 5% on a total of $1700.00 I have a small business some pay with cash I need to calculate the taxes in reverse I have tried to total X.15=255. -1700=1545.00 x.08=123.60 1545.x.05=77.25 77.25+123.60=285.85. Can you help with formula that the government might like Thank you Janet Hi Janet, The answer is dependent on where you live. Suppose the before tax price is X dollars. Since you are in Ontario the GST is 5% of X, that is 0.05 × X dollars and likewise the PST is 8% of X or 0.08 × X dollars. Thus the after tax price is X + (0.05 × X) + (0.08 × X) = X + 0.13 × X = 1.13 × X Since you know the after tax price is$1700 you have

1.13 × X = 1700

and hence

X = 1700/1.13 = 1504.42 dollars.

Now you can calculate the taxes

GST: 0.05 × $1504.42 =$75.22
PST: 0.08 × $1504.42 =$120.35

In Quebec the PST is charged on the price after you add the GST.

I hope this helps,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.