Algebra 1 word question about involving quadric equations and functions

label Algebra
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Kedra earned $192 from the sale of flower arrangements that she had made. If she had charged $8 more apiece, she could have sold two fewer arrangements and still have earned the same amount. How many arrangements did Kedra sell. 

Jun 3rd, 2015

Thank you for the opportunity to help you with your question!

Let she sold x arrangements... @ $y each

hence    xy = 192   from here we can write  y = 192/x

Next if shw would have sold (x-2) pieces at $(y+8)  then 

(x-2)(y+8) = 192

solving we get   (x-2)( 192/x +8) = 192

or we can write , (x-2) (192+8x) = 192x

or, 192x+8x^2 -384 -16x =192x

or , 8x^2 -16x-384 =0

we can write it as 8(x+6)(x-8) = 0   hence x = -6  or x = 8

since she can not sell Negative arrangments there fore we will omit x = -6

Answer = she sold  8 arrangements

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Jun 3rd, 2015

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