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Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?"The salesperson says that her commission is 5.5% of the selling price.How much money will the store get from the sale of the couch with the information from question 3 (final price: $27.23)? (Round tothe nearest cent.)

Answer :

We know that the final price of the couch is $27.23. This includes the 5.5% commission for the salesperson.

Then, we can define X as the price before commission.

The commission of the salesperson becomes 5.5/100*X=0.055X.

Then, the final price can be written as:

[tex]\begin{gathered} 27.23=X+0.055X \\ 1.055X=27.23 \\ X=\frac{27.23}{1.055} \\ X\approx25.81 \end{gathered}[/tex]

This price before commission X=25.81 is what the store get from the sale.

We can calculate the commission as:

[tex]0.055X=0.055\cdot25.81\approx1.42[/tex]

If we add the commission to the price before commission, we get:

[tex]25.81+1.42=27.23[/tex]

Answer: $25.81

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