SOLUTION: Hi :) I've been working on this question for a few hours but nothing seems right: You buy a toy for $x and sell it for $19.24. You incur a loss of x%. Find x. I think I ha

Algebra ->  Equations -> SOLUTION: Hi :) I've been working on this question for a few hours but nothing seems right: You buy a toy for $x and sell it for $19.24. You incur a loss of x%. Find x. I think I ha      Log On


   

Question 684181: Hi :)
I've been working on this question for a few hours but nothing seems right:
You buy a toy for $x and sell it for $19.24. You incur a loss of x%. Find x.
I think I have to make a trinomial but I can't seem to get the first few steps right.
Thanks for your help!
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Hi :)
I've been working on this question for a few hours but nothing seems right:
You buy a toy for $x and sell it for $19.24. You incur a loss of x%. Find x.
I think I have to make a trinomial but I can't seem to get the first few steps right.
Thanks for your help!

Since it was purchased for $x, then loss = $(x - 19.24)
Since loss = x – 19.24, then loss %, or x% = %28x+-+19.24%29%2Fx ---- x%2F100+=+%28x+-+19.24%29%2Fx
x%5E2+=+100%28x+-+19.24%29 ------ Cross-multiplying
x%5E2+=+100x+-+1924
x%5E2+-+100x+%2B+1924+=+0
(x – 26)(x – 74) = 0 ------- Factoring the trinomial

x, or cost of toy = $highlight_green%2826%29, and a loss of x%, or highlight_green%2826%29% was incurred on the sale of the toy for $19.24

OR

x, or cost of toy = $highlight_green%2874%29, and a loss of x%, or highlight_green%2874%29% was incurred on the sale of the toy for $19.24

You can do the check!!

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