   SEARCH HOME Math Central Quandaries & Queries  Question from Juanda: Hello, 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,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.