A reverse PST calculation

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Question from Manning:

Hi, I'm a manufacturing contractor in Saskatoon. The way to calculate PST for us is using total contract amount x 70% then 5%.
For example, contract amount of $100 x 70% x 5% = $3.5 (PST). The subtotal is using contract amount + PST.
$100 + $3.50 = $103.50.

If you only know the subtotal is $103.50 including PST, how do you reverse calculation to get the contract amount?

Hi,

Some algebra shows what to do. If the contract amount is $\$C$ then since $0.70 \times 0.05 = 0.035,$ the PST is

$0.035 × \$C.$

Hence the subtotal, which I'll call $S is

$\$S = \$C + 0.035 \times \$C = 1.035 \times \$C.$

This is a one step calculation to find the subtotal $S,

$\$S = 1.035 \times \$C.$

But you have $\$S$ and you want $\$C$ so in the equation above divide both sides by 1.035 to get

$\$C = \frac{\$S}{1.035}.$

Thus for the example you sent where $\$S = \$103.50,$

$\$C = \frac{\$103.50}{1.035} = \$100.00.$

I hope this helps,
Harley

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