# Show that $\frac{a_1}{b_1}+\frac{a_2}{b_2}+…+\frac{a_n}{b_n} \geq n$

Let $a_1$, $a_2$,..., $a_n$ be the sequence of positive numbers, and let $b_1$, $b_2$,..., $b_n$ be any permutation of the first sequence. Show that $$\frac{a_1}{b_1}+\frac{a_2}{b_2}+...+\frac{a_n}{b_n} \geq n$$

This is a preparation Question PUTNAM contest. The theme of the section is "inequality". I can not make the problem from inequality. Is anyone is able give me a hint (using inequalities)?

Hint: AM-GM. Note that the product of our fractions is $1$.