2004 AMC 10B Problem 2

The numbers $70$ through $79$ give $10$ with a $7$ in the tens place. The numbers $17, 27, \ldots, 97$ give $9$ with a $7$ in the units place. Since $77$ is counted twice, the total is $10 + 9 - 1 = 18.$ Thus, the correct answer is B.