Math CentralQuandaries & 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.

Stephen La Rocque.

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