Question

To determine whose statements about the equations are correct, we will need to solve each of the equations and identify their solution sets.

**Equation A:**
\(3(4 - 5h) - 7 = -12 + 2h\)

1. Distribute on the left side:
\(12 - 15h - 7 = -12 + 2h\)
2. Simplify:
\(5 - 15h = -12 + 2h\)
3. Rearrange to isolate \(h\):
\(5 + 12 = 15h + 2h\)
\(17 = 17h\)
\(h = 1\)

**Solution Set of Equation : \( h = 1 \)

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**Equation B:**
\(2(p - 3) - 1 = 6p + 142\)

1. Distribute on the left side:
\(2p - 6 - 1 = 6p + 142\)
2. Simplify:
\(2p - 7 = 6p + 142\)
3. Rearrange to isolate \(p\):
\(-7 - 142 = 6p - 2p\)
\(-149 = 4p\)
\(p = -\frac{149}{4}\)

**Solution Set of Equation B**: \( p = -\frac{149}{4} \)

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**Equation C:**
\(23v - 3 + 83 = -1\)

1. Combine like terms:
\(23v + 80 = -1\)
2. Rearrange to isolate \(v\):
\(23v = -1 - 80\)
\(23v = -81\)
\(v = -\frac{81}{23}\)

**Solution Set of Equation C**: \( v = -\frac{81}{23} \)

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Now let's summarize the solutions:
- Equation A has the solution \( h = 1 \).
- Equation B has the solution \( p = -\frac{149}{4} \).
- Equation C has the solution \( v = -\frac{81}{23} \).

Now, we can analyze the statements:

1. **Tamara**: "Equation A and Equation C have the same solution." - **False** (Solutions are \(h = 1\) and \(v = -\frac{81}{23}\)).
2. **Payton**: "Equation B and Equation C have the same solution." - **False** (Solutions are \(p = -\frac{149}{4}\) and \(v = -\frac{81}{23}\)).
3. **Krish**: "All three have the same solution." - **False** (All three equations have different solutions).
4. **Haruki**: "None of the equations have the same solution." - **True** (All three equations have different solutions).

Based on this analysis, the correct answer is **Haruki**.