Explanation
From the statement, we know that the store:
0. buys instruments and then sells them for 30% more than they paid,
,
1. during a 20% sale, the store offers a clarinet for $93.60.
(1) From point 1, we know that the relation between the original price (Po) and the selling price (Ps) is given by:
[tex]P_s=(1+0.3)*P_o=1.3*P_o\Rightarrow P_o=\frac{P_s}{1.3}.[/tex]
(2) From point 2, we know that the relation between the final price with the discount (P_f) and the selling price without the discount (Ps) is:
[tex]P_f=(1-0.2)*P_s=0.8*P_s\Rightarrow P_s=\frac{P_f}{0.8}=\frac{\text{ \$93.60}}{0.8}=\text{ \$117.}[/tex]
(3) Finally, replacing the value of Ps in the equation of point (1), we find that the original price of the instrument was:
[tex]P_o=\frac{\text{ \$117}}{1.3}=\text{ \$90.}[/tex]Answer
The store paid approximately $90 for the clarinet.
