Question

If the equation 7x + 13y = N, has exactly 7 positive integral solutions. Find the maximum value of N​

Answer 1

Given : equation 7x + 13y = N, has exactly 7 positive integral solutions

To find :   the maximum value of N​

Solution:

7x + 13y = N,  

7 & 13 are co prime

LCM of 7 & 13  = 91

=> 91 * 8  will give 7 positive integral solutions

728

here are 7 Solutions

x = 13    y = 49

x = 26 ,    Y = 42

x = 39     y  = 35

x = 52    y  = 28

x = 65    y  = 21

x =  78   y  = 14

x  = 91   y =  7

91 * 6 = 546 will give 7 integral solution if 0 is also considered as solution

0

x = 0 ,    Y = 42

x = 13     y  = 35

x = 26    y  = 28

x = 39    y  = 21

x =  52   y  = 14

x  = 65   y =  7

x = 78    y = 0

maximum value of N​ = 728   will give    exactly 7 positive integral solutions.

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