Let's solve the equation step by step. The given equation is:

$21 + \frac{2}{3}t = 50 - \frac{11}{12}t$

Step 1: Eliminate the fractions by finding a common denominator.

The common denominator for $\frac{2}{3}$ and $\frac{11}{12}$ is 12. Multiply the entire equation by 12 to eliminate the fractions:

$12 \times 21 + 12 \times \frac{2}{3}t = 12 \times 50 - 12 \times \frac{11}{12}t$

This simplifies to:

$252 + 8t = 600 - 11t$

Step 2: Move the terms involving $t$ to one side and constants to the other.

Add $11t$ to both sides:

$252 + 8t + 11t = 600$

This simplifies to:

$252 + 19t = 600$

Step 3: Isolate the variable $t$.

Subtract 252 from both sides:

$19t = 348$

Finally, divide by 19:

$t = \frac{348}{19} = 18.32$

Final Answer:

$t = 18.32$

Would you like further details or have any questions?

Here are some related questions:

1. How do you solve linear equations with fractions?
2. What are the steps to isolate a variable in an equation?
3. How can you check if your solution to an equation is correct?
4. What methods can be used to simplify fractions in equations?
5. What are common mistakes when solving equations with fractions?

Tip: Always simplify fractions as early as possible to make calculations easier.