We have a final price of $631 that includes the sales tax.
We can then decompose this final price (FP) in two terms: original price (OP) and the sales tax (ST).
[tex]FP=OP+ST[/tex]As the sales tax is 7.7% of the original price, we can write:
[tex]\begin{gathered} FP=OP+ST \\ FP=OP+0.077OP \\ FP=1.077*OP \end{gathered}[/tex]As we know the final price we can calculate the original price as:
[tex]\begin{gathered} FP=1.077*OP \\ OP=\frac{FP}{1.077}=\frac{631}{1.077}=585.89 \end{gathered}[/tex]Answer: the original price was $585.89.
