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Suppose that a and b are integers such that 3b = 8 - 2a. How many of the first six positive integers must be divisors of 2b + 30?

 May 5, 2022
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b =  (8 - 2a) / 3

 

For  b to be an integer, a must be   1 , 4 , 7 , 10 .... 

 

2b + 30  =      2 ( b + 15)   =   2 [ (8 -2a) / 3  + 15 ]  =   2 [ 53 - 2a] / 3

 

Divisors  =    1 , 2 ,  6

 

 

cool coolcool 

 May 5, 2022

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