   SEARCH HOME Math Central Quandaries & 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.\$

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.