SOLUTION: Positive integers B and C satisfy B(B-C) = 17. What is the value of C?

Question 238038: Positive integers B and C satisfy B(B-C) = 17. What is the value of C?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Solving this problem requires more logic than Algebra. The key is to recognize that 17 is a prime number. And the only factors a prime number has are 1 and itself (or -1 and the negative of itself. But the problem says B and C are positive so we will ignore the negatives.)

So B and (B-C) must be 1 and 17. We just have to figure out which is which. Since B and C are positive, B must be larger than (B-C). So
B = 17 and (B-C) = 1
And we can solve this for C:
(17-C) = 1
17 = 1 + C
16 = C

So B = 17 and C = 16.
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