If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true?

  • A q = 18
  • B p<1
  • C p = 18
  • D q<1
jamb 2010mathematics

The correct answer is A. q = 18

Let’s solve the equation given: 18(p+q) = (18+p)q

Expanding both sides, we get:

18p + 18q = 18q + pq

Rearranging the terms, we get:

18p - pq = 0

Factoring out p, we get:

p(18 - q) = 0

Setting each factor equal to zero gives the solutions to the equation:

p = 0 or q = 18

However, the problem states that p and q are non-zero numbers. Therefore, p cannot be zero.

So, the only solution is q = 18.

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