   SEARCH HOME Math Central Quandaries & Queries  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.