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Alex spent 35 dollars on cookies. If the cookies were 1 dollar cheaper, he would be able to buy 4 more cookies. How many cookies did alex buy? Reduce the problem to a quadratic equation in terms of c the number of cookies by eliminating p the price of a cookie. 

 Jul 16, 2021
 #1
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Let  p  be  the original  price per cookie  and  c  the  number bought

 

So

cp  =  35   ⇒  p   =  35 / c

 

And

 

(c + 4)) ( p -1)     = 35

 

(c + 4)  (  35/c - 1)  =  35

 

35  +  140/c  - c  -  4  =  35

 

-c +  140/c   +  31  =  35

 

-c + 140/c   -  4  =  0                        multipy  through  by  -c

 

c^2  + 4c   - 140    =   0                   factor

 

(c  + 14)  ( c - 10)  =  0

 

The  second factor set to  0  and solved  for c  =  10

 

He originally  bought  10 cookies    and  their  cost  was  $3.50  each  =   $35

 

So  4 more  at  a  $1  price  reduction per coookie  gives.......

 

14  (2.50)  =  $35    

 

 

cool cool cool

 Jul 16, 2021
 #2
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thanks chris :)

 Jul 16, 2021

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