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Jim's Market couldn't keep Crunchy Critter Crackers in stock. Jim started with 300 boxes but everyone wanted them. The first day Jim sold 6 boxes, and on the second day he sold 14 boxes. Each day 8 more boxes were sold than the day before. So after two days, he had sold 20 boxes. If he kept selling the crackers at this rate, when would Jim run out of Crunchy Critter Crackers?

 Jun 14, 2022
 #1
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This  is the sum of an arithmetic series

 

n ( a1  + a1 + (n -1) d)  / 2  >  300

 

a1  = 6  = the first term

n = the number of days

d  = the common difference =  8       

 

So we have

 

n ( 6 + 6  + (n-1) * 8 )   /  2 >  300

 

n ( 12 + 8n - 8)  >  600

 

n ( 4 + 8n)  >  600

 

4n + 8n^2  > 600       divide through by 4

 

2n^2 + n >  150

 

2n^2 + n - 150  >  0

 

Solve this

 

2n^2  + n  -150  = 0

 

Using the Quadratic Formula

 

n   =        -1 + sqrt ( 1^2  - 4 (2) (-150) )                -1 + sqrt ( 1201)

              _________________________ =        _______________ ≈  8.41

                               2 * 2                                                4

 

He will  run out  sometime  during the 9th day

 

 

cool cool cool

 Jun 15, 2022

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