Let's analyze each equation step by step to determine their solution sets.
### Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \]
First, we simplify the left side:
\[ 3(4 - 5h) = 12 - 15h \]
So,
\[ 12 - 15h - 7 = -12 + 2h \]
This simplifies to:
\[ 5 - 15h = -12 + 2h \]
Now, combine like terms:
\[ 5 + 12 = 15h + 2h \]
which results in:
\[ 17 = 17h \]
Dividing by 17 gives:
\[ h = 1 \]
### Equation B:
\[ 2(p - 3) - 1 = 6p + 142 \]
First, we simplify:
\[ 2p - 6 - 1 = 6p + 142 \]
This becomes:
\[ 2p - 7 = 6p + 142 \]
Rearranging the equation:
\[ -7 - 142 = 6p - 2p \]
This simplifies to:
\[ -149 = 4p \]
Dividing by 4 gives:
\[ p = -\frac{149}{4} \]
### Equation C:
\[ 23v - 3 + 83 = -1 \]
Combine like terms:
\[ 23v + 80 = -1 \]
Now, isolate \(v\):
\[ 23v = -1 - 80 \]
This simplifies to:
\[ 23v = -81 \]
Dividing by 23 gives:
\[ v = -\frac{81}{23} \]
### Summary of Solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{149}{4} \)
- Equation C: \( v = -\frac{81}{23} \)
Now let's analyze the statements:
- Tamara says A and C have the same solution. (False, \(1 \neq -\frac{81}{23}\))
- Payton says B and C have the same solution. (False, \(-\frac{149}{4} \neq -\frac{81}{23}\))
- Krish says all three have the same solution. (False)
- Haruki says that none of the equations have the same solution. (True)
### Conclusion:
Haruki is correct. None of the equations have the same solution.