To determine who is correct regarding the solutions to the equations, we'll first solve each equation separately.
### **Equation A:**
\[ 3(4-5h) - 7 = -12 + 2h \]
First, distribute:
\[ 12 - 15h - 7 = -12 + 2h \]
Combine like terms:
\[ 5 - 15h = -12 + 2h \]
Rearranging gives:
\[ 5 + 12 = 15h + 2h \]
\[ 17 = 17h \]
Divide both sides by 17:
\[ h = 1 \]
### **Equation B:**
\[ 2(p-3) - 1 = 6p + 142 \]
Distribute:
\[ 2p - 6 - 1 = 6p + 142 \]
Combine like terms:
\[ 2p - 7 = 6p + 142 \]
Rearranging gives:
\[ -7 - 142 = 6p - 2p \]
\[ -149 = 4p \]
Divide both sides by 4:
\[ p = -\frac{149}{4} \]
### **Equation C:**
\[ 23v - 3 + 83 = -1 \]
Combine like terms:
\[ 23v + 80 = -1 \]
Subtract 80 from both sides:
\[ 23v = -81 \]
Divide both sides by 23:
\[ v = -\frac{81}{23} \]
### **Review of Solutions:**
- **Equation A:** \( h = 1 \)
- **Equation B:** \( p = -\frac{149}{4} \)
- **Equation C:** \( v = -\frac{81}{23} \)
### **Analyzing the Claims:**
1. **Tamara:** Claims A and C have the same solution. (False: \( h \neq v \))
2. **Payton:** Claims B and C have the same solution. (False: \( p \neq v \))
3. **Krish:** Claims A, B, and C all have the same solution. (False: All values are different)
4. **Haruki:** Claims none of the equations have the same solution. (True: \( h \), \( p \), and \( v \) are all unique)
### **Conclusion:**
Haruki is correct; none of the equations have the same solution.