   SEARCH HOME Math Central Quandaries & Queries  Question from Kim: If I have spent $1700 what portion is GST now that the rate has dropped to 5%? Hi Kim. I have two methods for you. First method. Let's say before GST, your subtotal is x dollars. Then the total is this amount (x) PLUS the gst amount (5% of x). So the Total = x + 5%(x) = 1x + 0.05x = 1.05x, because 5% means 0.05. Thus, if your total is$63, then
$63 = 1.05x and we solve for x by dividing both sides by 1.05: x =$63/1.05
x = $60. So the pre-tax subtotal was$60. The GST is the difference between this and the aftertax total: $63 -$60 = $3. You can see that to find the total before GST all you need to do is divide by 1.05. Do that for$1700 and you have your subtotal. Then subtract that from $1700 to get the amount of GST you paid. Second Method. Let G = the GST amount and let S = the subtotal amount and let T = the grand total including GST. Then T = G + S. But the GST is 5% of the subtotal, so G = 5%(S). This means G = 0.05 S or 20G = S (I found that by multiplying both sides by 20). Well if S = 20G, and T = G + S, then T = G + 20G which is just 21G. So we've proved that T = 21G. If I divide both sides by 21, I get T/21 = G. Say my total is$63 including GST. This is T, so
G = T / 21 = $63 / 21 =$3.

The GST is \$3.

Simply put, if you have the total including GST and want to know how much GST you paid, then just divide by 21.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.