Math CentralQuandaries & Queries


Question from Duncan:

HI - I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost.
i.e.) I know I paid $\$400$ GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated!

Hi Duncan,

Suppose $T$ is the total in dollars to which the GST is applied and that the GST is $P\%.$ To calculate the amount of GST paid you would take $P\%$ of $T.$Thus

\[\mbox{GST paid } = \frac{P}{100} \times T.\]

In your question you know the GSP paid and you want to know $T.$ Solving the equation above for $T$ I get

\[T = \frac{\mbox{GST paid}}{\frac{P}{100}}.\]

In your example where the GST paid is $\$400$ and assuming the GST is 5% I get

\[T = \frac{400}{0.05} = 8,000 \mbox{ dollars.}\]


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