Let's solve the equations to determine who is correct about their solution sets.
Equation A: \[ 3(4 - 5h) - 7 = -12 + 2h \] Expanding the left side: \[ 12 - 15h - 7 = -12 + 2h \] Simplifying: \[ 5 - 15h = -12 + 2h \] Bringing the \(h\) terms together: \[ 5 + 12 = 15h + 2h \] \[ 17 = 17h \] Dividing by 17: \[ h = 1 \]
Equation B: \[ 2(p - 3) - 1 = 6p + 142 \] Expanding the left side: \[ 2p - 6 - 1 = 6p + 142 \] Simplifying: \[ 2p - 7 = 6p + 142 \] Bringing the \(p\) terms together: \[ -7 - 142 = 6p - 2p \] \[ -149 = 4p \] Dividing by 4: \[ p = -\frac{149}{4} \]
Equation C: \[ 23v - 3 + 83 = -1 \] Combining the constants: \[ 23v + 80 = -1 \] Subtracting 80 from both sides: \[ 23v = -1 - 80 \] \[ 23v = -81 \] Dividing by 23: \[ v = -\frac{81}{23} \]
Now we have the solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{149}{4} \)
- Equation C: \( v = -\frac{81}{23} \)
Next, we compare the solutions:
- Tamara's claim (Equation A and C have the same solution) is incorrect.
- Payton's claim (Equation B and C have the same solution) is incorrect.
- Krish's claim (all three have the same solution) is incorrect.
- Haruki's claim (none of the equations have the same solution) is correct.
Therefore, Haruki is correct that none of the equations have the same solution.