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

3
3

1

Answer 1

To identify the number of equations that have the same solution set, we'll solve each equation for its variable and see if they yield the same solution.

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

Expanding both sides:

\[ 135f - 315 = 100f - 200 \]

Rearranging:

\[ 135f - 100f = 315 - 200 \]
\[ 35f = 115 \]
\[ f = \frac{115}{35} = \frac{23}{7} \]

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

Rearranging:

\[ 59g = 79 + 2 \]
\[ 59g = 81 \]
\[ g = \frac{81}{59} \]

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

Expanding both sides:

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

Rearranging:

\[ 4h - 3h = -3 + 8 \]
\[ h = 5 \]

### Summary of Solutions:
1. Equation A has the solution \( f = \frac{23}{7} \).
2. Equation B has the solution \( g = \frac{81}{59} \).
3. Equation C has the solution \( h = 5 \).

All solutions are different.

Thus, the number of equations that have the same solution set is **none**.

**Correct response: none**