Final answer:
To find the number of 3-digit numbers that contain at least one 7, subtract the number of 3-digit numbers that don't contain any 7's from the total number of 3-digit numbers.
Step-by-step explanation:
To find the number of 3-digit numbers that contain at least one 7, we can count the total number of 3-digit numbers and subtract the number of 3-digit numbers that don't contain any 7's.
The total number of 3-digit numbers is 900 (from 100 to 999).
The number of 3-digit numbers that don't contain any 7's is found by counting the options for each digit position. For the hundreds place, there are 9 possible digits (1-9), for the tens place there are 9 possible digits (0-9 except 7), and for the ones place there are also 9 possible digits (0-9 except 7). Therefore, there are a total of 9 * 9 * 9 = 729 3-digit numbers that don't contain any 7's.
Finally, we can subtract the number of 3-digit numbers that don't contain any 7's from the total number of 3-digit numbers to find the number of 3-digit numbers that contain at least one 7. Therefore, the number of 3-digit numbers that contain at least one 7 is 900 - 729 = 171.