Let's illustrate this technique by assuming that a vending machine contains only items that are subject to a sales tax of 7%. For a recent month the vending machine receipts were $481.50. This $481.50 includes the amounts received for sales of product and for the sales tax on these products. A little algebra will allow us to calculate how much of the $481.50 is the true sales amount and how much is the sales tax on the products sold.
Let S = the true sales of products (excluding the sales tax), and let 0.07S = the sales tax on the true sales. Since the true sales + the sales tax = $481.50, we can state that S + 0.07S = $481.50. Next we combine the terms and have 1.07S = $481.50. We solve for S by dividing $481.50 by 1.07. Hence the amount of true sales is $450. The 7% of sales tax on the true sales is $31.50 ($450 X 0.07). Now let's prove these amounts: $450 of sales + $31.50 of sales tax = $481.50, the total amount of receipts from the vending machine.
Let's try another example. If the total amount of receipts including a 7% sales tax is $32,100, the true sales amount will be $30,000 ($32,100 divided by 1.07). The sales tax on the true sales will be 0.07 X $30,000 = $2,100. Our proof is $30,000 of sales + $2,100 of sales tax = $32,100. The accounting entry in general journal form it will be: debit Cash $32,100; credit Sales $30,000; credit Sales Tax Payable $2,100.
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