# An algebra problem by David Altizio

Algebra Level 3

Let $$p$$ and $$q$$ be real numbers with $$|p|<1$$ and $$|q|<1$$ such that $p+pq+pq^2+pq^3+\cdots=2\qquad\text{and}\qquad q+qp+qp^2+qp^3+\cdots=3.$ What is $$100pq$$?

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