Respuesta :
Answer:
The clearance price is $17.28.
The clearance price will not give the store any profit.
Step-by-step explanation:
We have been given that a store pays a manufacturer $20 for a hat. To make a profit, the store prices the hat 60% higher than the amount they paid.
The price of the hat after increasing the price by 60% will be:
[tex]\text{Price of the hat after an increase of 60\%}=20+(\frac{60}{100}*20)[/tex]
[tex]\text{Price of the hat after an increase of 60\%}=20+(0.60*20)[/tex]
[tex]\text{Price of the hat after an increase of 60\%}=20+12[/tex]
[tex]\text{Price of the hat after an increase of 60\%}=32[/tex]
So, the price of hat after the increase of 60% will be $32.
As the sale reduces the price of hat by 10%, so the price of hat after sale will be:
[tex]\text{Price of the hat after sale of 10\%}=32-(\frac{10}{100}*32)[/tex]
[tex]\text{Price of the hat after sale of 10\%}=32-(0.10*32)[/tex]
[tex]\text{Price of the hat after sale of 10\%}=32-3.2[/tex]
[tex]\text{Price of the hat after sale of 10\%}=28.8[/tex]
So the price of hat after 10% sale will be $28.8.
As the clearance sale reduces the price by 40%, so price of hat after clearance sale will be 28.8 minus 40% of 28.8.
[tex]\text{Price of the hat after clearance sale}=28.8-(\frac{40}{100}*28.8)[/tex]
[tex]\text{Price of the hat after clearance sale}=28.8-(0.40*28.8)[/tex]
[tex]\text{Price of the hat after clearance sale}=28.8-11.52[/tex]
[tex]\text{Price of the hat after clearance sale}=17.28[/tex]
Therefore, the clearance price is $17.28.
As store has purchased the hat from manufacturer for $20 and sold it $17.28, therefore, the store will not have a profit.
