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Sally has a bagful of candy. She arranges it into an A by B grid, but she has 2A+B candies leftover . Her big sister Rita comes along and says, "I can do better than that!" Rita neatly arranges the candies into a 5A-4 by B-1/3 grid and has none leftover. What is the maximum number of candies in Sally's bag?

 May 6, 2019
 #1
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(5A - 4) (B - 1) / 3  - AB  = 2A + B

 

(5A - 4) (B - 1) - 3AB  = 6A + 3B

 

5AB - 4B - 5A+ 4 - 3AB  = 6A + 3B

 

2AB - 7B - 11A + 4  =  0

 

B (  2A - 7)  = 11A - 4            or            

 

B  =   ( 11A - 4)                                     

         ________                                           

           (2A - 7)                                               

 

We have two possibilities

 

A     B

4    40

38   6

 

The max  candies is either

 

(5(4) - 4) ( 40-1)/3   =  16 * 13  =  208     or

(5(38) - 4) (6 - 1)/3    = 310

 

So.....310 candies

 

cool cool cool

 May 6, 2019

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