Respuesta :
The right answer for the question that is being asked and shown above is that: "A: Sale of 10% off and a successive discount of 10% off." The store that would let you pay the least amount for an item that is priced $360 is the Store A.
The correct answer is Store A: Sale of 10% off and a successive discount of 10% off.
Further explanation:
Discount is the reduction of amount in the cost price of any item.
The following formula for discount can be used when the rate of discount and the cost price is given.
[tex]\boxed{{\text{Discount}}=\left( {\dfrac{{{\text{rate of discount}}}}{{100}}}\right)\times{\text{cost price}}}[/tex]
The following formula for selling price can be used when the discount and the cost priceis given.
[tex]\boxed{{\text{Selling price}}={\text{Cost price}}-{\text{Discount}}}[/tex]
Given:
The price of an item is [tex]\boxed{\$360}[/tex].
Calculation:
Store A is allowing 10% off and then allowing a successive discount of 10%.
The first discount of an item by the use of the formula can be calculated as,
[tex]\begin{aligned}{\text{discount}}&=\left( {\frac{{10}}{{100}}}\right)\times 360\\&= 36\\\end{aligned}[/tex]
Now, the selling price after allowing the first discount is,
[tex]\begin{aligned}{\text{Selling price}}&={\text{360}}-36\\&=324\\\end{aligned}[/tex]
The successive discount on the item can be calculated as,
[tex]\begin{aligned}{\text{discount}}&=\left( {\frac{{10}}{{100}}}\right)\times324\\&=32.4\\\end{aligned}[/tex]
Now, the selling price after allowing second discount is,
[tex]\begin{aligned}{\text{Selling price}}&={\text{324}}-32.4\\&=291.6\\\end{aligned}[/tex]
Therefore, the amount we have to pay to Store A is [tex]\boxed{\$291.6}[/tex].
Store B is giving 15% off with no additional discount.
The discount of an item by the use of the formula can be calculated as,
[tex]\begin{aligned}{\text{discount}}&=\left( {\frac{{15}}{{100}}}\right)\times360\\&=54\\\end{aligned}[/tex]
Now, the selling price after allowing discount can be calculated as,
[tex]\begin{aligned}{\text{Selling price}}&={\text{360}}-54\\&=306\\\end{aligned}[/tex]
Therefore, the amount we have to pay to Store B is [tex]\boxed{\$306}[/tex].
Store C is giving $35 off and then allowing a successive discount of 10%.
Now, the selling price after allowing first discount can be calculated as,
[tex]\begin{aligned}{\text{Selling price}}&={\text{360}}-35\\&=325\\\end{aligned}[/tex]
The successive discount on the item can be calculated as,
[tex]\begin{gathered}{\text{discount}}=\left( {\frac{{10}}{{100}}}\right)\times325\\=32.5\\\end{gathered}[/tex]
Now, the selling price after deducting second discount can be calculated as,
[tex]\begin{aligned}{\text{Selling price}}&={\text{325}}-32.5\\&=292.5\\\end{aligned}[/tex]
Therefore, the amount we have to pay to Store C is [tex]\boxed{\$292.5}[/tex].
It can be clearly seen that if we buy an item which is priced at $360 from Store A then we have to pay least amount of $291.6.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Profit and Loss
Keywords: Percentage , profit , loss, discount, cost price, selling price, marked price, rate of discount, amount, succesive discount, reduction, maximum, price .
