Question

You are charged $631 for a new bicycle. Assume sales tax is 7.7%, what was the original price for the bicycle? (round your answer to the nearest cent)

Answer 1

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).

`FP=OP+ST`

As the sales tax is 7.7% of the original price, we can write:

`\begin{gathered} FP=OP+ST \\ FP=OP+0.077OP \\ FP=1.077*OP \end{gathered}`

As we know the final price we can calculate the original price as:

`\begin{gathered} FP=1.077*OP \\ OP=(FP)/(1.077)=(631)/(1.077)=585.89 \end{gathered}`

Answer: the original price was $585.89.