Mathematics

Question

A music player was marked down by 1/4 of the original price.
a. If the sales price is $128, what is the original price?
b. If the music player was marked up by 1/2 before it was placed on the sales floor, what was the price that the store paid for the player?
c. What is the difference between the discount price and the price that the store paid for the music player?

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1 Answer

  • Answer:

    Part A) 170.66$ would be the original price.

    Part B) 256$ would be the price that the store paid for the music player.

    Part B) What you need to balance is your markup, meaning how much to raise your price, and your markdown or discount, meaning, how to much to decrease prices.

    Step-by-step explanation:

    Part A) Determining the Original Price

    Note: when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

    So, a music player was marked down by 1/4 of the original price, and we have to calculate the original price if the sales price is $128.

    Let 'p' be the original price

    As a music player was marked down by 1/4 of the original price

    So, Markdown = 1/4p

    As the sales price is $128

    As the Sale price = [tex]p - \frac{p}{4}[/tex] ⇒ [tex]\frac{3p}{4}[/tex]

    [tex]128 = \frac{3p}{4}[/tex]

    [tex]552 =3p[/tex]

    [tex]p =170.66[/tex]          

    Hence, 170.66$ would the original price.

    Part B) Determining the Price that the store paid for the music player

    When an amount is added to the cost price of a product or commodity in order to determine the selling price, it means the the product or commodity is being marked up.

    So, as the music player was marked up by 1/2 before it was placed on the sales floor and we have to determine the price that store paid for the player.

    So, dividing the original price by 2 and adding the result to the original price would give us the price that store had to pay for the music player.

    As the original price is 170.66.

    So, the price that the store paid for the music player can be calculated as:

    price = 170.66 + 170.66/2

    price = 170.66 + 85.33

    price = 255.99$  ≈ 256$

    Therefore, 256$ was the price that the store paid for the music player.

    Part C) Determining the difference between the discount price and the price that the store paid for the music

    For example, let suppose you are a shopkeeper and have a jeans fabric business. You want to make money from it. But, in order to earn money from selling jeans fabric, you have to make sure that your price must be at the right value price both in terms of generating money and also giving your customer a great value for the money to given them a decent deal.

    What you need to balance is your markup, meaning how much to raise your price, and your markdown, meaning, how to much to decrease prices.

    In business, the conditions may never always remain favorable due to certain circumstance, hence bad days. Sometimes, the conditions get ideal for business, hence good days.

    As I earlier sated that when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

    For example, the cost price of 1 Jeans fabric is 10$, and you want to earn profit. So, you mark up your fabric to 30$.  As $30 is $20 more than $10. So, markup value will be 2. In terms of percentage, it means you have a markup of 200%.

    But, due to certain issues, your sales are being effected due to certain condition. In order to not affect the sales, you want to markdown the price - a kind of discount. Your starting price was $30 and want to decrease the price to $20. It means the difference is $10. So, you have made a markup or given a discount of $30/$10 = 0.33. In terms of percentage, it is around 33%. So, you have given the discount of 33% to hope for the great sales.

    So, in the question, when the music player was marked down by 1/4 of the original price, it means the discount of 1/4 of the original price was provided. As the sale price was $128, and original price was $170.66. So, discount of 1/4 or 25% was offered.

    As the original price was $170, and it was marked up by 1/2 by the owner or creator of music player before it was placed on the sales floor. So, 256$ was the price that the store paid for the music player.

    Keywords: markdown, markup, discount, price

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