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Look b4 U leap (Posted on 2020-10-02)

Find a solution to the equation:
29x + 30y + 31z = 366

Rem: x,y,z must be positive

See The Solution Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

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Explanation to Puzzle Answer: Method 1

| Comment 5 of 8 |

(In reply to Puzzle Answer by K Sengupta)

29x+30y+31z=366

=> 30(x+y+z)+z-x= 366

=> x+y+z+ (z-x)/30 = 12 +6/30

Thus, x+y+z= 12

z-x = 6

This yields:

y+2z=18 and, 2x+y=6

Now, 2x+y=6, y+2z=18 has the positive integer solutions as:

x 2 1

y 2 4

z 8 7

Consequently, (x, y, z) = (2, 2, 8), (1, 4, 7) are the only possible solutions.

Posted by K Sengupta on 2022-06-14 23:26:08

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