Math CentralQuandaries & Queries


Question from Juanda:


I know the customer cost with tax and I know the sales tax.
How do I find out the customer cost prior to the added sales tax?

Thank you

HI Juanda,

I assume that you know the sales tax as a percentage.

Suppose the customer cost before the tax is added is $\$C,$ the customer cost after the tax is added is $\$T,$ and the tax is $p\%.$ Then if you are the sales clerk and know $C$ then you calculate $T$ by

\[C + \frac{p}{100} \times C = T.\]

The left side can be simplified to obtain

\[C \left( 1 + \frac{p}{100}\right) = T.\]

Dividing both sides by $1 + \large \frac{p}{100}$ gives

\[C = \frac{T}{1 + \frac{p}{100}}. \]

For example where I live in Saskatchewan Canada most items have a 5% Provincial Sales Tax and a 5% Goods and Services Tax and hence the tax rate is 10%. Thus if I bought an item and paid $\$14.25$ tax included then the cost before the tax was $\large \frac{\$14.25}{1.10} \normalsize = \$12.95.$

I hope this helps,

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