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)
Responses

2
2

none
none

1
1

3

1 answer

To determine how many equations share the same solution set, we need to solve each equation and find their respective solutions.

Solve Equation A:

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

Start by distributing both sides: \[ 135f - 315 = 100f - 200 \]

Next, isolate \( f \): \[ 135f - 100f = 315 - 200 \] \[ 35f = 115 \] \[ f = \frac{115}{35} = \frac{23}{7} \]

Solve Equation B:

\[ 59g - 2 = 79 \]

Add 2 to both sides: \[ 59g = 81 \] Now, isolate \( g \): \[ g = \frac{81}{59} \]

Solve Equation C:

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

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

Isolate \( h \): \[ 4h - 3h = -3 + 8 \] \[ h = 5 \]

Summary of Solutions:

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

Each equation has a different solution set:

  • \( f = \frac{23}{7} \)
  • \( g = \frac{81}{59} \)
  • \( h = 5 \)

Thus, none of the equations share the same solution set.

The correct response is: none.