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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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Respuesta :

Answer:

a) $170.67

b) $198

c) $27.33

Step-by-step explanation:

a)Let the original price be $[tex]x[/tex] ;

  • When it's price is marked down by [tex]\frac{1}{4}^{th}[/tex] of the original price , then the new price [tex]y[/tex] becomes :
  • [tex]y=x-x*\frac{1}{4}\\y=x-\frac{x}{4}\\y=\frac{4x-x}{4}\\y=\frac{3x}{4};[/tex]
  • Now from the question, the new price [tex]y=128[/tex];

Thus,

  • [tex]\frac{3x}{4}=128\\x=128*\frac{4}{3}\\x=170.67;[/tex]

Thus the original price is $170.67.

b)

If the music player was marked up before the sale, then the original price is increased. That is ,

Let's say the new original price to be [tex]x_1[/tex];

∴

[tex]x_1=x+\frac{1}{2}*x\\x_1=\frac{3x}{2}[/tex]

Now this price is marked down by [tex]\frac{1}{4}^{th}[/tex].

∴

[tex]y=x_1-\frac{x_1}{4} \\\\y=\frac{3x_1}{4} \\\\x_1=\frac{3x}{2} \\\\y=\frac{3*\frac{3x}{2} }{4} \\\\y=\frac{9x}{8} \\y=198;[/tex]

Thus the price the store paid will be $198;

c)

The difference is $198-$170.67 = $27.33

katlynne908

Answer: C! :) hope this helped! ✨

Step-by-step explanation:

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