# 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.

1
by sweetysiri92
can i use a linear model?

2014-11-08T12:07:45+05:30

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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

thanx n u r welcom. nice of u