Introduction
To find the number of two-digit numbers that are divisible by 3, we need to understand the concept of divisibility by 3.

Divisibility Rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, the number 123 is divisible by 3 because 1+2+3=6 which is divisible by 3.

Method
To find the number of two-digit numbers that are divisible by 3, we need to consider all the possible two-digit numbers. There are 90 two-digit numbers (10 to 99).

We can then apply the divisibility rule for 3 to each of the two-digit numbers and count the ones that are divisible by 3.

Calculation
Let's consider all the two-digit numbers from 10 to 99:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
90, 91, 92, 93, 94, 95, 96, 97, 98, 99.

We can see that the numbers that are divisible by 3 are:

12, 15, 18,
21, 24, 27,
30, 33, 36, 39,
42, 45, 48,
51, 54, 57,
60, 63, 66, 69,
72, 75, 78,
81, 84, 87, 90, 93, 96, 99.

Answer
There are 30 two-digit numbers that are divisible by 3.