Math CentralQuandaries & Queries


Question from janet:

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

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,

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