Math CentralQuandaries & Queries


Question from REBECCA, a parent:

Hi, I have a total of $\$300.$
What is the subtotal & GST?
How do I work backwards?

Hi Rebecca,

Suppose the GST is r%, here in Canada the GST is 5% so I would use $r = 0.05$.

Think about going forward. If the subtotal were $\$S$ then to find the total you would add $\$S$ and $r \times \$S$ to get the total $\$T$. Thus

\[\$T = (1 + r) \times \$S\]

To find $\$S$ you need to divide both sides by $(1 + r)$ to get

\[\$S = \frac{\$T}{1 + r}\]

so when the total is $\$300$ the subtotal is $\frac{\$300}{1 + r}$ and the GST is $r \times \$S.$


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