Question

Martha picked out a pair of shoes she wanted and brought them to the front of the store to pay. The cashier told her that the shoes were on sale for $30$% off the original price. She rang up the sale price plus $5$% sales tax, so Martha ended up paying 58.80$ for the shoes. What was the original price for the shoes?

• A. 70$
• B. 75$
• C. 80$
• D. 85$
• E. 90$

Answer 1

The correct option is C 80$Letoriginalpricebe$x$Givensaleof$30\%$onoriginalcost$\Rightarrow x-\dfrac { 30 }{ 100 } \times x\Rightarrow x-\dfrac { 3 }{ 10 } x\Rightarrow \dfrac { 10x-3x }{ 10 } =\dfrac { 7x }{ 10 } $Furthersalestaxof$5\%$wasadded.So,$\dfrac { 7x }{ 10 } +\dfrac { 5 }{ 100 } \times \dfrac { 7x }{ 10 } \Rightarrow \dfrac { 7x }{ 10 } +\dfrac { 35x }{ 1000 } \Rightarrow \dfrac { 700x+35x }{ 1000 } =\dfrac { 735x }{ 1000 } $Asperproblem,wehave$\dfrac { 735 }{ 1000 } x=58.80\Rightarrow x=\dfrac { 58800 }{ 735 } =80$Originalpriceoftheshoeis$\$80$.