To determine how many of the given equations have the same solution set, we need to solve each equation and analyze their solutions.
Equation A:
\[ 45(3f - 7) = 25(4f - 8) \]
Expanding both sides: \[ 135f - 315 = 100f - 200 \]
Rearranging gives us: \[ 135f - 100f = 315 - 200 \] \[ 35f = 115 \] \[ f = \frac{115}{35} = \frac{23}{7} \]
So the solution for Equation A is \( f = \frac{23}{7} \).
Equation B:
\[ 59g - 2 = 79 \]
Adding 2 to both sides: \[ 59g = 81 \]
Dividing by 59: \[ g = \frac{81}{59} \]
So the solution for Equation B is \( g = \frac{81}{59} \).
Equation C:
\[ -2(4 - 2h) = -3(1 - h) \]
Distributing gives us: \[ -8 + 4h = -3 + 3h \]
Rearranging gives us: \[ 4h - 3h = -3 + 8 \] \[ h = 5 \]
So the solution for Equation C is \( h = 5 \).
Now let's summarize the solutions:
- Equation A has \( f = \frac{23}{7} \)
- Equation B has \( g = \frac{81}{59} \)
- Equation C has \( h = 5 \)
Since all three equations have different solutions, they do not have the same solution set.
Thus, the final answer is: none.
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