Math CentralQuandaries & Queries


Question from Bev:

Total sales revenues are 116391.38 this amount includes 5% GST and 80% of this amount includes a 7% provincial tax. The other 20% is PST exempt. GST is included in all. How do I figure the PST I owe?

Hi Bev,

A little bit of algebra will get you what you need.

Suppose the total revenues before any taxes is $\$T.$ To calculate the total sales after taxes you need to do two things.

  1. First apply the $5\%$ GST to get a GST of $0.05 \times \$T.$

  2. Now the PST. $80 \%$ of the sales before taxes is $0.80\times \$T$ and $7\%$ of this is $0.07 \times 0.80 \$T = 0.056 \times \$T.$

Thus the total revenue including taxes is $\$T + 0.05 \times \$T + 0.056 \times \$T = 1.106 \times \$T.$ But you know this is $\$116 391.38$ so

\[1.106 \times \$T = \$116 391.38\]

Dividing both sides by 1.106 yields

\[\$T = \frac{\$116 391.38}{1.106} = \$105 236.33\]

Finally, what is the PST? It is $7\%$ of $80\%$ of $\$T.$


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