Algebra worksheet asking students to determine if given equations are true or false for specified variable values.

To solve the problem, we need to evaluate each equation with the given value of the variable and determine whether the statement is true or false. Let's go through each one step by step.

1. \( y + 5 = 17 \), \( y = 22 \)

- Substitute \( y = 22 \) into the equation:
\[
22 + 5 = 27
\]
- The result is 27, not 17.
- False

2. \( 4x = 24 \), \( x = 6 \)

- Substitute \( x = 6 \) into the equation:
\[
4 \times 6 = 24
\]
- The result is 24, which matches the equation.
- True

3. \( n \div 7 = 3 \), \( n = 21 \)

- Substitute \( n = 21 \) into the equation:
\[
21 \div 7 = 3
\]
- The result is 3, which matches the equation.
- True

4. \( s - 13 = 21 \), \( s = 34 \)

- Substitute \( s = 34 \) into the equation:
\[
34 - 13 = 21
\]
- The result is 21, which matches the equation.
- True

5. \( 20 \times y = 300 \), \( y = 160 \)

- Substitute \( y = 160 \) into the equation:
\[
20 \times 160 = 3200
\]
- The result is 3200, not 300.
- False

6. \( n + 40 = 92 \), \( n = 50 \)

- Substitute \( n = 50 \) into the equation:
\[
50 + 40 = 90
\]
- The result is 90, not 92.
- False

7. \( 27 = 3m \), \( m = 9 \)

- Substitute \( m = 9 \) into the equation:
\[
3 \times 9 = 27
\]
- The result is 27, which matches the equation.
- True

8. \( 7 + t = 21 \), \( t = 11 \)

- Substitute \( t = 11 \) into the equation:
\[
7 + 11 = 18
\]
- The result is 18, not 21.
- False

9. \( x - 8 = 24 \), \( x = 32 \)

- Substitute \( x = 32 \) into the equation:
\[
32 - 8 = 24
\]
- The result is 24, which matches the equation.
- True

10. \( n + 24 = 61 \), \( m = 45 \)

- There seems to be a typo here. The variable in the equation is \( n \), but the given value is for \( m \). Assuming it should be \( n = 45 \):
- Substitute \( n = 45 \) into the equation:
\[
45 + 24 = 69
\]
- The result is 69, not 61.
- False

Final Answers:

1. False
2. True
3. True
4. True
5. False
6. False
7. True
8. False
9. True
10. False

\[
\boxed{\text{False, True, True, True, False, False, True, False, True, False}}
\]