<Question>
Two-thirds of the students at Baker Middle School take music. There are 834 students who take music. How many students are there at Baker Middle School?
</Question>

<think>
<Plan_1>
Okay, let's see. The problem says that two-thirds of the students at Baker Middle School take music, and there are 834 students who take music. We need to find the total number of students at the school.

Hmm, so if two-thirds of the total students equal 834, then maybe I can set up an equation. Let me think. Let's denote the total number of students as, say, x. Then two-thirds of x would be (2/3)*x. And that equals 834.
So the equation is (2/3)x = 834. To find x, I need to solve for it. So, multiply both sides by the reciprocal of 2/3, which is 3/2. That would give x = 834 * (3/2).

Let me calculate that.
First, 834 divided by 2 is 417. Then 417 multiplied by 3 is 1251. So, x should be 1251.

Wait, let me check again. If 2/3 of 1251 is 834, then 1251 divided by 3 is 417, and 417 times 2 is 834.

But let me make sure I didn't make any mistakes here. Another way to think about it: if two-thirds correspond to 834, then one-third would be half of that, which is 417. So, three-thirds would be 417 times 3, which is 1251.

Alternatively, using algebra step by step:

<prompt_1.1> Use an algebraic method to solve the equation (2/3)x = 834 step by step. </prompt_1.1>

Another check: Let's say the total number of students is 1251. Two-thirds of them take music. So, 1251 divided by 3 is 417. Then 417 multiplied by 2 is 834.
That's exactly the number given.

Wait, but maybe I should consider if there's any possibility of rounding errors or if the numbers are exact. The problem states 834 students take music, which is exactly two-thirds. So, if 834 is exactly two-thirds, then the total must be an integer.
Since 834 divided by 2 is 417, which is an integer, and 417 multiplied by 3 is 1251, which is also an integer.
</Plan_1>

<Execution_1>
<execution_1.1>
(2/3)x = 834  
Multiply both sides by 3: 2x = 834 * 3  
Calculate 834 * 3: 2x = 2502  
Divide both sides by 2: x = 2502 / 2  
x = 1251
</execution_1.1>
</Execution_1>

<Final_answer>
Therefore, the total number of students at Baker Middle School is $\boxed{1251}$.
</Final_answer>
</think>