Question

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

Answer 1

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**.