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The sales tax on an item with a retail price of $972 is $77.76. Create a variational model that gives the retail price,y , in terms of the sales tax,x , and use it to determine the retail price of an item that has a sales tax $92.34.

Answer :

kvnmurty
Sales man decides his sale price initially as marked price MP and gives a discount D%. Let us say the salesman's final decided selling price (excluding tax) is  P.

          Tax amount = Sales_tax% * P = x
If we say Sales_tax % is fixed as per laws, let us call it  C%.
 
         x = C% * P = P * C/100
        =>    P = 100 x /C

Retail Sale price =  RP = P + tax amount = 100 x /C + x
                       y = x (100/C+1) = (100+C) x / C

This is the linear relationship between the sales tax amount and the retail price.

      When x = $77.76, y = $972,
              => 100/C + 1 =  972/77.76  = 12.5
                 =>    C  =  100 / 11.5 = 8.695 

  Hence y = 12.5 x   is the relationship between  sales tax and  retail price.
          with sales tax percentage being C = 8.695%

      sales tax = $92.34 = x
           =>  retail price = y = 12.5 * $92.34  = $ 1, 154.25

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