Hi Tonya.

I'm uncertain whether you mean that the $275 includes the taxes or not, so I'll show you both ways.

$275 not including tax:
Unless you are in Quebec, GST and PST are applied to the pre-tax amount. In Quebec, people pay PST after GST is applied (so they pay tax on tax). So elsewhere the GST is (0.06)$275 = $16.50 and the PST is (0.07)$275 = $19.25. That does indeed total (0.13)$275 = $35.75.

$275 including taxes:
Outside Quebec (if you are in Quebec, read this earlier answer I wrote): You know that the tax plus the subtotal before taxes adds up to the total of $275. So (0.13)S + S = $275. This reduces to S = $275/1.13 = $243.36. The GST is (0.06) times the pre-tax subtotal: (0.06)$243.36 = $14.60 and the PST is (0.07)$243.36 = $17.04. Add these all together and you will get $275, the final total. In general, this "reverse calculation" looks like this:

• Pre-tax amount = (grand total) / (1 + PST rate + GST rate).
• PST amount = (PST rate) × (grand total) / (1 + PST rate + GST rate).
• GST amount = (PST rate) × (grand total) / (1 + PST rate + GST rate).
• Total taxes amount = (PST rate + GST rate) × (grand total) / (1 + PST rate + GST rate)
• PST amount = (PST rate)(grand total)/(1+PST rate+GST rate).

Be aware that in most provinces there are categories of goods and services that get one tax or the other but not both. So it partly also depends on what you spend the $275 on.

Hope this helps,
Stephen.