I need help with #3
2 answers:
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.
The given equation is
We need to solve the equation for q.
<u>Value of q:</u>
The value of q can be determined by solving the equation for q.
Thus, subtracting both sides of the equation by r, we get;
Now, dividing both sides of the equation by b, we have;
Simplifying the terms, we get;
Therefore, the value of q is
Hence, Option B is the correct answer.