Question

A mattress underwent the following changes in price before being removed from the store.

20%
Markdown
35%
Markup
24%
Markdown
13%
Markup
31%
Markdown

If the final price of the mattress was $227.83, what was the original price of the mattress, to the nearest dollar? Round all dollar values to the nearest cent.

Answer 1

Since we are given with the final price already, we calculated for the initial price backwards.
  (1)                          227.83 = (1 - 0.31)x₁
                                   x₁ = 330.19

  (2)                          330.19 = (1 + 0.13)x₂
                                     x₂ = 292.20

   (3)                           292.29 = (1 - 0.24)x₃
                                      x₃ = 384.48
 
   (4)                           384.48 = (1 + 0.35)x₄
                                       x₄ = 284.80
   
   (5)                           284.80 = (1 - 0.20)x₅
                                        x₅ = 355.99 or 356

Therefore, the original price of the mattress is ~ $356. 

Answer 2

Answer: The answer is A or 356

Step-by-step explanation: I got 100% on test