SOLUTION: A test is worth 200 points.Th test consist of true and false questions worth 6 points each and multiple choice questions are worth 13 points each.how many multiple choice questions

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Question 1026238: A test is worth 200 points.Th test consist of true and false questions worth 6 points each and multiple choice questions are worth 13 points each.how many multiple choice questions are on the test and true and false questions?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
This is a linear Diophantine equation given by 6x + 13y = 200, where x = # of true or false questions, and y = # multiple choice questions.
A particular solution is x%5B0%5D+=+16 and y%5B0%5D+=+8.
All solutions are given by x+=+x%5B0%5D%2B13n=16%2B13n and y=y%5B0%5D-6n+=+8-6n, where n is any integer.
==> There are three possible solutions:
x = 3, y = 14;
x = 16, y = 18;
x = 29, y = 2.
Note: The solution was made possible by the fact that gcd(6,13) = 1 divides 200.