Question

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. Later, a sale reduces the price of the hat by 10%. Finally, a clearance sale reduces the sale price by 40%. What is the clearance price? Will this price five the store a profit?

Answer 1

The clearance price is $17.28.

The clearance price will not give the store any profit.

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:

`\text{Price of the hat after an increase of 60\%}=20+((60)/(100)*20)`

`\text{Price of the hat after an increase of 60\%}=20+(0.60*20)`

`\text{Price of the hat after an increase of 60\%}=20+12`

`\text{Price of the hat after an increase of 60\%}=32`

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:

`\text{Price of the hat after sale of 10\%}=32-((10)/(100)*32)`

`\text{Price of the hat after sale of 10\%}=32-(0.10*32)`

`\text{Price of the hat after sale of 10\%}=32-3.2`

`\text{Price of the hat after sale of 10\%}=28.8`

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.

`\text{Price of the hat after clearance sale}=28.8-((40)/(100)*28.8)`

`\text{Price of the hat after clearance sale}=28.8-(0.40*28.8)`

`\text{Price of the hat after clearance sale}=28.8-11.52`

`\text{Price of the hat after clearance sale}=17.28`

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.