Identify the number of equations that have the same solution set.

Equation A: 45(3f−7)=25(4f−8)


Equation B: 59g−2=79


Equation C: −2(4−2h)=−3(1−h)


(1 point)
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1 answer

To determine the number of equations that have the same solution set, we'll need to solve each equation.

Equation A:
\[ 45(3f - 7) = 25(4f - 8) \]

Distributing on both sides: \[ 135f - 315 = 100f - 200 \]

Bringing like terms together: \[ 135f - 100f = 315 - 200 \] \[ 35f = 115 \] \[ f = \frac{115}{35} = \frac{23}{7} \]

Equation B:
\[ 59g - 2 = 79 \]

Adding 2 to both sides: \[ 59g = 81 \] \[ g = \frac{81}{59} \]

Equation C:
\[ -2(4 - 2h) = -3(1 - h) \]

Distributing: \[ -8 + 4h = -3 + 3h \]

Rearranging the equation: \[ 4h - 3h = -3 + 8 \] \[ h = 5 \]

Now, we have the solutions for each equation:

  • Equation A: \( f = \frac{23}{7} \)
  • Equation B: \( g = \frac{81}{59} \)
  • Equation C: \( h = 5 \)

Since each equation has a different solution set, the number of equations that share the same solution set is none.

Final response: none.